Monday, 15 January 2024

We discuss the structure and properties of a class of anomalous high-energy states of matter-free U(1) quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. We demonstrate the formation of such scars from the superposition of exact zero modes in a particular U(1) gauge theory. A class of these, called sublattice scars, seem to be perfectly structured if a particular local observable is probed even though these states are high-energy eigenstates. A "triangle relation" that connects some anomalous zero modes with other states with nonzero integer eigenvalues will be discussed.

We address the fate of Fermi liquids in Floquet bands coupled to heat reservoirs.

For fermionic baths, we will show that periodically driven Fermions are described by a periodic Gibbs ensemble in which the Fermi Dirac occupation is replaced by a stair-case-like function which has several step discontinuities, leading to a "Floquet Fermi Liquid” state that contains several Fermi surfaces enclosed inside each other. We will discuss several properties of these states such as quantum oscillations, how to tune their van-Hove singularities without changing the electron density, and clarify and old controversy in optoelectronics by demonstrating that current rectification is possible when the frequency of the drive is within the optical gap of the metal.

For bosonic baths, we will demonstrate the existence of a "Floquet Non-Fermi liquid state" that has no analogue in equilibrium. It features "higher order Floquet Fermi surfaces” where the occupation in momentum space displays cusp-like non-analyticities, but without an associated jump or quasiparticle residue. More intriguingly, the sharpness of these higher order Floquet Fermi surfaces survives even at finite temperatures, implying that this Floquet Non-Fermi Liquid remains quantum critical at finite temperatures, unlike equilibrium Fermi and Non-Fermi liquids where temperature acts as a relevant perturbation that renders the fluid classical with exponentially decaying correlations at sufficiently large distances.

The field of thermodynamics is one of the crown jewels of classical physics. Thanks to the advent of experiments in cold atomic systems with long coherence times, our understanding of the connection of thermodynamics to quantum statistical

mechanics has seen remarkable progress.

Extending these ideas and concepts to the non-equilibrium setting is a challenging topic, in itself of perennial interest. Here, we present perhaps the simplest non-equilibrium class of quantum problems, namely Floquet systems, i.e. systems, whose Hamiltonians depend on time periodically, H(t + T) = H(t). For these, there is no energy conservation, and hence not even a natural concept of temperature.

We find that certain structures from equilibrium thermodynamics are lost, while entirely new non-equilibrium phenomena can arise, including a spectacular spatiotemporal `time-crystalline' form of order, recently observed experimentally on Google AI's sycamore NISQ platform.

References: for an introductory overview, see Nature Physics 13, 424–428 (2017). For an in-depth review, see arxiv:1910.10745. NISQ experiment: Nature 601, 531 (2022).

Quantum many-body scars are notable as nonthermal, low-entanglement states that exist at high energies. We use attractively interacting dysprosium gases to create scar states that are stable enough to be driven into a strongly nonlinear regime while retaining their character [1]. We uncover an emergent nonlinear many-body phenomenon, the apparent transmutation of attractive interactions into repulsive interactions. Using measurements of the momentum and the rapidity distributions [2], we find how the kinetic and the kinetic+interaction energies, respectively, evolve after quenching the confining potential. Although the bare interactions are attractive, the kinetic energy decreases while the kinetic+interaction energy increases as the gas is compressed, i.e., the atoms behave as if they repel each other. The missing kinetic energy is quantified by benchmarking the experimental results against generalized hydrodynamics calculations. We present evidence that the missing "phantom" energy is carried by undetected, very high-momentum atoms.

References:

[1] K. Yang, Y. Zhang, K.-Y. Li, K.-Y. Lin, S. Gopalakrishnan, MR, and B. L. Lev, Phantom energy in the nonlinear response of a quantum many-body scar state, arXiv:2308.11615.

[2] K.-Y. Li, Y. Zhang, K. Yang, K.-Y. Lin, S. Gopalakrishnan, MR, and B. L. Lev, Rapidity and momentum distributions of one-dimensional dipolar quantum gases, Phys. Rev. A 107, L061302 (2023).

Tuesday, 16 January 2024

I will discuss the dynamics of monitored systems combining the ingredients of unitary evolution, measurements, and adaptive classical control. I will present various novel dynamical phases and phase transitions that arise in these systems, ranging from entanglement and teleportation phase transitions to "learnability" transitions in the ability to reconstruct quantum information from measurements. I will also discuss experimental realizations of these phenomena in noisy quantum processors.

Eigenstate thermalization hypothesis (ETH) explains why an isolated quantum system eventually thermalizes, but it does not tell us much about the timescale of the onset of thermalization. Since the time evolution is unitary, all the eigenvalues of the time evolution operator lie on the unit circle in complex plane. It means that we cannot estimate the thermalization timescale by looking at eigenvalues of the time evolution operator.

In this talk, I argue that an open-system analysis based on the Lindblad quantum master equation gives an estimate of the thermalization timescale of the isolated system [1]. More specifically, we consider a kicked Ising chain under bulk dissipation and investigate the Liouvillian gap, which is the spectral gap of the generator of the dynamics, in the weak dissipation limit. We show that the Liouvillian gap can remain finite even in the weak dissipation limit if the thermodynamic limit is taken first. This finite value of the Liouvillian gap in the weak dissipation limit gives the exponential decay rate of the isolated system. This result is reminiscent of Ruelle-Pollicott resonances in classical chaos. Indeed, we argue that the finite Liouvillian gap in the weak dissipation limit is interpreted as a quantum Ruelle-Pollicott resonance.

For static systems with the time-independent Hamiltonian, a special care is needed. I also explain how we can extract exponential decays hidden in the unitary time evolution of a static system.

[1] T. Mori, arXiv:2311.10304

The field of thermodynamics is one of the crown jewels of classical physics. Thanks to the advent of experiments in cold atomic systems with long coherence times, our understanding of the connection of thermodynamics to quantum statistical

mechanics has seen remarkable progress.

Extending these ideas and concepts to the non-equilibrium setting is a challenging topic, in itself of perennial interest. Here, we present perhaps the simplest non-equilibrium class of quantum problems, namely Floquet systems, i.e. systems, whose Hamiltonians depend on time periodically, H(t + T) = H(t). For these, there is no energy conservation, and hence not even a natural concept of temperature.

We find that certain structures from equilibrium thermodynamics are lost, while entirely new non-equilibrium phenomena can arise, including a spectacular spatiotemporal `time-crystalline' form of order, recently observed experimentally on Google AI's sycamore NISQ platform.

References: for an introductory overview, see Nature Physics 13, 424–428 (2017). For an in-depth review, see arxiv:1910.10745. NISQ experiment: Nature 601, 531 (2022).

Decoherence is the main obstacle to quantum information processing and fault-tolerant quantum computing. That's why it is extremely important to explore ways to suppress the decoherence of a quantum system. The constituents of a generic interacting many-body system usually decohere under their dynamics but some sophisticated (integrable) interaction can lead to long-lived emergent quasiparticles, for example, edge Majorana zeromode of a Kitaev chain. The notion of strong zero mode (SZM) was extended to systems with genuine (yet integrable) interaction but their existence in non-integrable systems has been a long-standing open question. In this talk, I will discuss how local Floquet engineering can be used to help emerge an SZM in a non-integrable system of staggered Heisenberg chain with a global field. Individual sites can not be dynamically frozen even by the most optimal choice of drive parameters. Interestingly, a special sequence of optimally driven sites can stabilize an SZM, enhancing the decoherence time of the boundary spin exponentially in system size.

I will consider closed quantum many-body systems, time-evolving by unitary dynamics, so fully isolated from any external environment. One basic issue is whether or not a large such system can serve as a bath (or environment) for itself, bringing all of its subsystems to thermal equilibrium with each other via the system’s unitary quantum dynamics. When a system does do this, that is “thermalization”. Exceptions to thermalization include “quantum many-body

scars” and various types of integrability or near-integrability; many-body Anderson localization is one type of integrability.

As one simple example of integrability and the transition/crossover to near-integrability and thermalization, I will discuss a weakly interacting gas (time permitting). This also serves as an example of “Fock-space many-body localization”.

Then I will focus on many-body localization in one-dimensional systems with only short-range interactions and hoppings. I will review our present understanding of the phase diagram of such systems and discuss two key phenomena that are important in such systems, namely the “avalanche” instability, and many-body resonances. This will serve as an introduction to later lectures by John Imbrie.

**Refs:**

Crowley and Chandran, arXiv:2012.14393

Morningstar, et al., arXiv:2107.05462

Sels, arXiv:2108.10796

Bulchandani, et al., arXiv:2112.14762

Long, et al., arXiv:2207.05761

Ha, Morningstar and Huse, arXiv:2301.04658

Wednesday, 17 January 2024

In this talk, we shall discuss a driven fermi chain and show that such a system displays prethermal Hilbert space fragmentation (HSF) at specific drive frequencies. The signature of such fragmentation and their experimental implications shall be discussed. We shall also show, taking an interacting finite Hatano-Nelson chain as example, that HSF can provide a route to realization of real eigenspectra of non-Hermitian quantum systems.

In recent years, superconducting qubits have emerged as one of the leading platforms for quantum computation and simulation. We utilize these Noisy Intermediate Scale Quantum (NISQ) processors to study nonequilibrium quantum dynamics and simulate quantum phases of matter. I will present some of our recent works in studying robustness of bound states of photons [1], measurement-induced quantum information phases [2], and the universality classes of dynamics in the 1D Heisenberg chain [4]. A goal for this talk is to provide a sense of what NISQ discoveries to anticipate and a time scale for them.

[1] Morvan et al., Nature 612, 240–245 (2022)

[2] Hoke et al., Nature 622, 481–486 (2023)

[3] Rosenberg et al., Arxiv.org/abs/2306.09333

Over the past two decades our understanding of the charge and heat transport properties of graphene has evolved progressively as the quality of the graphene devices improved. A key crossover occurs when the scattering between electrons themselves become more frequent than the scattering between electrons and disorder. In this regime, the electrons gas behaves as a hydrodynamic fluid, whose properties exhibit emergent universalities close to the charge neutrality point. In this talk, I shall present some new experimental result on the electrical and thermal transport measurements in graphene devices of unprecedented electrical mobility (> 1 million cm2/V.s). I shall show that the transport in such graphene devices is unique in multiple ways, ranging from unconventional functional dependence of the dc conductivity on carrier density to giant violation of the Wiedemann-Franz law, where effective Lorenz number varies over six orders of magnitude with carrier density. We find that the transport properties of ultra-clean graphene close to charge neutrality are quantitatively consistent with that of a hydrodynamic Dirac fluid.

We will discuss how quantum jumps affect localized regimes in driven-dissipative disordered many-body systems featuring a localization transition. We introduce a deformation of the Lindblad master equation that interpolates between the standard Lindblad and the no-jump non-Hermitian dynamics of open quantum systems. We probe both the statistics of complex eigenvalues of the deformed Liouvillian and dynamical observables of physical relevance. We show that reducing the number of quantum jumps, achievable through realistic post-selection protocols, can promote the emergence of the localized phase. We will also discuss eigenvector correlations across the localization transition in non-Hermitian power-law banded random matrices.

I will discuss how one can define chaos in Hamiltonian systems through adiabatic transformations. I will explain how complexity of the adiabatic gauge potential, which is the generator of such transformations, is behind seemingly different phenomena such as chaos, ergodicity, and integrability, long time response of physical observables, emergence of conservation laws, Schrieffer–Wolff transformations, hydrodynamic response, counter-diabatic driving and other phenomena. Using this probe I will argue that integrable and ergodic regimes are always separated by an intermediate universal chaotic but non-ergodic phase characterized by slow glassy-type response. This intermediate regime can be termed as maximally chaotic, because the adiabatic transformations have the largest complexity. The fact that systems are most chaotic near integrability is in fact well known from our everyday experience as weakly interacting nearly integrable gases with large Reynolds numbers often lead to very chaotic turbulent flows, while stronger interactions lead to simpler laminar flows. I will argue that this intermediate regime was mistakenly identified in the past as a thermodynamically stable many body localized phase and will discuss some common mistakes made in the MBL literature (both analytical and numerical). I will also explain the mechanism of instability of localized integrals of motion through the operator growth. I will illustrate this maximally chaotic regime with other examples both quantum and classical systems including Floquet systems close to integrability. At the end I will mention some open questions.

Understanding the out-of-equilibrium dynamics of a closed quantum system driven across a quantum phase transition is an important problem with widespread implications for quantum state preparation and adiabatic algorithms. While the quantum Kibble-Zurek mechanism elucidates part of these dynamics, the subsequent and significant coarsening processes lie beyond its scope. Here, we develop a universal description of such coarsening dynamics---and their interplay with the Kibble-Zurek mechanism---in terms of scaling theories. Our comprehensive theoretical framework applies to a diverse set of ramp protocols and encompasses various coarsening scenarios involving both quantum and thermal fluctuations. Moreover, we highlight how such coarsening dynamics can be directly studied in today's "synthetic" quantum many-body systems, including Rydberg atom arrays, and present a detailed proposal for their experimental observation.

I will consider closed quantum many-body systems, time-evolving by unitary dynamics, so fully isolated from any external environment. One basic issue is whether or not a large such system can serve as a bath (or environment) for itself, bringing all of its subsystems to thermal equilibrium with each other via the system’s unitary quantum dynamics. When a system does do this, that is “thermalization”. Exceptions to thermalization include “quantum many-body

scars” and various types of integrability or near-integrability; many-body Anderson localization is one type of integrability.

As one simple example of integrability and the transition/crossover to near-integrability and thermalization, I will discuss a weakly interacting gas (time permitting). This also serves as an example of “Fock-space many-body localization”.

Then I will focus on many-body localization in one-dimensional systems with only short-range interactions and hoppings. I will review our present understanding of the phase diagram of such systems and discuss two key phenomena that are important in such systems, namely the “avalanche” instability, and many-body resonances. This will serve as an introduction to later lectures by John Imbrie.

**Refs:**

Crowley and Chandran, arXiv:2012.14393

Morningstar, et al., arXiv:2107.05462

Sels, arXiv:2108.10796

Bulchandani, et al., arXiv:2112.14762

Long, et al., arXiv:2207.05761

Ha, Morningstar and Huse, arXiv:2301.04658

Thursday, 18 January 2024

I will discuss the stability of prototypical quantum phenomena such as localization and edge modes in the presence of an environment. Focus will be on analogue quantum simulation in the Markovian regime described by a Lindbladian. I will highlight the distinction of the non-equilibrium states and their phase transitions from their isolated counterparts.

I will discuss our recently introduced information lattice as an intuitive way to organise entanglement or quantum information into scales. I will then show how this gives useful information about both localised states and thermalising dynamics and will outline an efficient algorithm for many-body dynamics. In the second part of the talk I will quickly advertise new results on ultraslow growth of number entropy in l-bit model of many-body localization.

I will discuss how one can define chaos in Hamiltonian systems through adiabatic transformations. I will explain how complexity of the adiabatic gauge potential, which is the generator of such transformations, is behind seemingly different phenomena such as chaos, ergodicity, and integrability, long time response of physical observables, emergence of conservation laws, Schrieffer–Wolff transformations, hydrodynamic response, counter-diabatic driving and other phenomena. Using this probe I will argue that integrable and ergodic regimes are always separated by an intermediate universal chaotic but non-ergodic phase characterized by slow glassy-type response. This intermediate regime can be termed as maximally chaotic, because the adiabatic transformations have the largest complexity. The fact that systems are most chaotic near integrability is in fact well known from our everyday experience as weakly interacting nearly integrable gases with large Reynolds numbers often lead to very chaotic turbulent flows, while stronger interactions lead to simpler laminar flows. I will argue that this intermediate regime was mistakenly identified in the past as a thermodynamically stable many body localized phase and will discuss some common mistakes made in the MBL literature (both analytical and numerical). I will also explain the mechanism of instability of localized integrals of motion through the operator growth. I will illustrate this maximally chaotic regime with other examples both quantum and classical systems including Floquet systems close to integrability. At the end I will mention some open questions.

The relaxation of observables to their nonequilibrium steady states in a disordered XX chain subjected to dephasing at every site has been intensely studied in recent years. We comprehensively analyze the relaxation of staggered magnetization, i.e., imbalance, in such a system, starting from the Néel initial state. We analytically predict emergence of several timescales in the system and extract results which match with large-system numerics without any extra fitting parameter until a universal timescale. An often reported stretched exponential decay is just one of the regimes which holds in a finite window of time and is therefore in fact not a true stretched exponential decay. Subsequently, the asymptotic decay of imbalance is governed by a power law irrespective of the disorder. We show that this emerges from the continuum limit of the low magnitude eigenspectrum of the Liouvillian. However, for finite systems, due to discreteness of the spectrum, the final phase of relaxation is governed by the relevant smallest Liouvillian gap.

Starting from a pure initial state, the local properties of chaotic many-body quantum systems are expected to quickly thermalize under unitary dynamics. The remaining evolution from local to global equilibrium is described by the classical equations of hydrodynamics. However, the advent of quantum simulator platforms has made it possible to measure not only local expectation values, but also their full quantum statistics, fluctuations and space-time correlations. In this talk, I will discuss a theory of diffusive fluctuations in chaotic many-body quantum systems, and establish its validity in random unitary quantum circuits with charge conservation. I will also discuss exceptions to this conventional behavior in integrable quantum spin chains, as well as Dirac fluids as a result of Lorentz invariance and particle-hole symmetry. In particular, I will argue that charge noise in the hydrodynamic regime of Dirac fluids is parametrically enhanced relative to that in conventional diffusive metals.

Friday, 19 January 2024

I will present new exotic topologies involving non-Abelian braiding of band nodes in multi-gap non-interacting systems. In systems with a real Bloch Hamiltonian band nodes can be characterised by a non-Abelian frame-rotation charge. The ability of these band nodes to annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps the sign of their charges can be changed. I will demonstrate new anomalous topological phases in out-of-equilibrium settings with no static counterparts, as well as ways for quantum simulators to probe them. In particular, I will construct an interferometry scheme allowing for probing these non-Abelian charges for the first time in ultracold atomic systems.

Slager, Bouhon, Ünal, arXiv:2208.12824

Breach, Slager, Ünal, arXiv:2401.01928

The Dicke model exhibits a rich variety of phase transitions. In this talk, we will try to cover the following points.

1) The usefulness of studying various eigenvector properties to characterize the phase transitions of the Dicke and the anisotropic Dicke model.

2) The effect of periodic and quasiperiodic drive on the Dicke model.

3) We introduce and study a disordered Dicke model. We show how analytical expressions for the quantum and thermal phase transitions can be obtained.

Kibble-Zurek theory (KZ) stands out as the most robust theory of defect generation in the dynamics of phase transitions. KZ utilizes the structure of equilibrium states away from the transition point to estimate the excitations due to the transition using adiabatic and impulse approximations. However, the actual nonequilibrium dynamics can lead to a qualitatively different scenario from KZ, as far correlations between the defects (rather than their densities) are concerned. For a quantum Ising chain, we show, this gives rise to a Gaussian spatial decay in the domain wall (kinks) correlations, while KZ would predict an exponential fall. We propose a simple but general framework on top of KZ, based on the "quantum coarsening" dynamics of local correlators in the supposed impulse regime.

Consider equal antiferromagnetic Heisenberg coupling between qubits sitting at the nodes of a complex, generally nonbipartite, network. We ask the question: What property of the network determines the net magnetization of the ground state? I will present strong evidence that graph heterogeneity, as measured by the presence of (disassortative) hubs, is the key ingredient to obtain nonzero total spin, not how frustrated the graph is. Additionally, the magnetization falls with the number of bonds per node. I will present statistics over different families of random graphs to corroborate this finding. I will also show how to construct frustrated non-random networks where the magnetization can be tuned over its entire range, across both continuous and discontinuous transitions, which can be solved exactly. These findings pose open questions and strongly motivate further exploration of frustrated magnetism beyond regular lattices.

Formation of doublons or onsite repulsively bound pairs of constituent particles in the quench dynamics of interacting particles is a highly non-trivial phenomenon. While a stable doublon is formed in the dynamics when the constituents are initially located on a single lattice site, non-local particles don't form a doublon due to strong interaction. However, we show a scenario where a non-trivial doublon can be formed in the dynamics of interacting non-local bosons of two different species. Furthermore, we show that such non-trivial doublons can also be formed in the QW of fermions in the framework of the Hubbard model. In the end we implement digital quantum circuit simulation to observe the dynamical doublon formation in a Noisy Intermediate-Scale Quantum (NISQ) device.

Being motivated by intriguing phenomena such as the breakdown of conventional bulk boundary correspondence and emergence of skin modes in the context of non-Hermitian (NH) topological insulators, we here propose a NH second-order topological superconductor (SOTSC) model that hosts Majorana zero modes (MZMs). Employing the non-Bloch form of NH Hamiltonian, we topologically characterize the above modes by biorthogonal nested polarization and resolve the apparent breakdown of the bulk boundary correspondence. Unlike the Hermitian SOTSC, we notice that the MZMs inhabit only one corner out of four in the two-dimensional NH SOTSC. Such localization profile

of MZMs is protected by mirror rotation symmetry and

remains robust under on-site random disorder. We extend the static MZMs into the realm of Floquet drive. We find anomalous $\pi$-mode following low-frequency mass-kick in addition to the regular $0$-mode that is usually engineered in a high-frequency regime. We further characterize the regular $0$-mode with biorthogonal Floquet nested polarization. Our proposal is not limited to the $d$-wave superconductivity only and can be realized in the experiment with strongly correlated optical lattice platforms.

Monday, 22 January 2024

Lie-Schwinger rotations provide a graphical framework for stepwise diagonalization of the Hamiltonian. Nonperturbative regions are controlled probabilistically with moment estimates and the Markov inequality.

The notion of scale-invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). We explore features of scale-invariant dynamics of survival probability and SFF at criticality, i.e., at eigenstate transitions from quantum chaos to localization. We show that, in contrast to the quantum chaotic regime, the quantum dynamics at criticality do not only exhibit scale invariance at late times, but also at much shorter times that we refer to as mid-time dynamics. Our results apply to both quadratic and interacting models.

We study a spin-1/2 model in one dimension in which there are three-spin Ising interactions and a transverse magnetic field. The model has a duality, and the self-dual point is a quantum critical point. The model has many unusual features which we have studied using exact diagonalization and the density matrix renormalization group (DMRG) method. At the critical point, the central charge c and the dynamical critical exponent z both turn out to be 1; hence the model must have a conformal field theory description. The model exhibits weak universality in the sense that the ratios of the critical exponents beta/nu and gamma/nu are the same as those of the transverse field Ising model and the four-state Potts model; hence the model at criticality belongs to the Ashkin-Teller family of models. In addition, DMRG provides some evidence that the model may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. The model has an exponentially large number of zero energy states. A subset of these states have an unusually low entanglement entropy between two halves of the system and hence qualify as many-body scars.

Finally, we find that the autocorrelation functions at sites close to one end of the system show some unusual features such as long-time oscillations with very slow decays.

Reference:

Udupa, Sur, Nandy, Sen and Sen, Phys. Rev. B 108, 214430 (2023)

Surprising signatures of anomalous spin transport have been reported in the spin-half Heisenberg spin chain at the isotropic point, in a number of recent work. The talk will discuss: (i) analogous results for classical integrable spin chains and (ii) properties of coupled Burgers equations that have been proposed as effective hydrodynamic descriptions of integrable spin chains.

I will discuss quantum state dynamics under a Floquet drive in generic many-body systems. In the first part, we present Fermi's golden rule (FGR) description for high frequencies [1]. We show that under Floquet heating, systems starting from a finite temperature are well approximated by a thermal ensemble for the effective Floquet Hamiltonian at a time-dependent temperature, and the FGR gives how the temperature increases. In the second part, we consider dynamics starting from the ground state of the effective Hamiltonian and show that the state is much more robust against Floquet heating than most other states. As a function of driving frequency, there is a transition-like behavior: Above a threshold driving frequency of O(1), the system remains to have finite energy density even after infinite Floquet cycles.

References: [1] T. N. Ikeda, A. Polkovnikov, Phys. Rev. B 104, 134308 (2021). [2] T. N. Ikeda, S. Sugiura, A. Polkovnikov, arXiv:2311.16217

Glassy dynamics have time-reparametrization `softness': glasses fluctuate, and respond to external perturbations, primarily by changing the pace of their evolution. Remarkably, the same situation also appears in toy models of quantum field theory such as the Sachdev-Ye-Kitaev (SYK) model, where the excitations associated to reparametrizations play the role of an emerging `gravity'. I describe here how these two seemingly unrelated systems share common features, arising from a technically very similar origin. Apart from the curiosity that this correspondence naturally arouses, there is also the hope that developments in each field may be useful for the other.

Understanding the nature of the transition from the delocalized to the many-body localized (MBL) phase is an important unresolved issue. To probe the nature of the MBL transition, we investigate the universal properties of single-particle excitations produced in highly excited many-body eigenstates of a disordered interacting quantum many-body system. Our results indicate that the MBL transition in a class of one-dimensional models of spinless fermions satisfy the CCFS bound for the critical exponent with which correlation length diverges at the transition. This holds true for all ranges of interactions among fermions and random onsite potential. MBL systems with quasiperiodic potentials satisfy a different universality class.

We show that generic disordered quantum wires, e.g. the XXZ-Heisenberg chain, do not exhibit many-body localization (MBL) - at least not in a strict sense within a reasonable window of disorder values. Specifically, computational studies of short wires exhibit an extremely slow but unmistakable flow of physical observables with increasing time and system size (`creep')

that is consistently directed away from (strict) localization. Our work sheds fresh light on delocalization physics: Strong sample-to-sample fluctuations indicate the absence of a generic time

scale, i.e., of a naive "clock rate"; however, the concept of an "internal clock" survives, at least in an ensemble sense.

We observe that the average entropy appropriately models the ensemble-averaged internal clock and reduces fluctuations. We take the tendency for faster-than-logarithmic growth of entanglement and smooth dependency on the disorder of all our observables within the entire simulation window as support for the cross-over scenario, discouraging an MBL transition within the traditional parametric window of computational studies.

Tuesday, 23 January 2024

I will describe competing effects on the density of nonperturbative regions. In the RG, isolated nonperturbative regions can be eliminated, while nearby ones have to be merged. Percolation estimates ensure that these regions are compact and rare, maintaining a minimum exponential decay rate and forestalling the avalanche mechanism.

We present a general protocol for driven many-body systems to generate a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. Our construction provides explicit effective Hamiltonians exhibiting the symmetry group in question for each prethermal regime. This allows us to imprint emergent quasiconservation laws hierarchically, enabling us to engineer various levels of symmetry breaking and order in Floquet matter. We provide explicit examples, including a spin chain realising the sequence SU(2) -> U(1) -> 2 -> E.

Understanding ergodicity and its breakdown in isolated quantum systems has been one of the central problems in recent times. A nonergodic behavior may arise in the presence of strong disorder leading to a many-body localization (MBL) phase or phases intermediate between ergodic and MBL, e.g., the so-called non-ergodic extended (NEE) phase. I will discuss real-space and Fock-space (FS) characterizations of ergodic, NEE, and MBL phases in an interacting quasiperiodic system, which possesses a mobility edge in the noninteracting limit. I will show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all single-particle excitations get localized in the MBL phase due to the MBL proximity effect. Based on a finite-size scaling analysis of the typical local FS self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the decay of the nonlocal propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.

The status of many-body localization (MBL) as of a stable non-ergodic phase of matter has been recently debated. In this talk, I will explore different interpretations of numerical results obtained with classical simulations of strongly disordered quantum many-body systems. Starting from the definition of MBL phase (which will be contrasted with an MBL regime), I will emphasize the role of interactions in slow dynamics of disordered many-body systems [1]. These findings will be linked to the spectral properties of many-body systems, as reflected by the so called Thouless time [2].

Subsequently, I will introduce a simple method of analysis of the ergodic-MBL crossover in exact diagonalization results. This method involves the introduction of two system size dependent disorder strengths: the first one delineates departure from ergodic behavior at given system size L, while the second one is the crossing point that estimates, at given L, the position of the putative ergodic-MBL transition. I will present results of this method for 1D disordered systems: Heisenberg spin chain [6] (and compare these results with earlier interpretations [4,5], constrained spin chains [6], and Floquet models [7]. Finally, I will draw comparisons between the observed finite size drifts at the ergodic-MBL crossover in interacting many-body systems and analytically demonstrated phase transition in dynamical properties of encoding-decoding circuits [8].

Overall, this talk aims to shed light on the ongoing discussions surrounding the MBL phase and its characterization in disordered many-body systems.

[1] PS, J. Zakrzewski, Phys. Rev. B 105, 224203 (2022)

[2] PS, D. Delande, J. Zakrzewski, Phys. Rev. Lett. 124, 186601 (2020)

[3] PS, M. Lewenstein, J. Zakrzewski, Phys. Rev. Lett. 125, 156601 (2020),

[4] V. Oganesyan, D. Huse, Phys. Rev. B 75, 155111 (2007)

[5] D. Luitz, N. Laflorencie, F. Alet, Phys. Rev. B 91, 081103(R) (2015)

[6] PS, E. Lazo, M. Dalmonte, A. Scardicchio, J. Zakrzewski, Phys. Rev. Lett. 127, 126603 (2021),

[7] PS, M. Lewenstein, A. Scardicchio, J. Zakrzewski, Phys. Rev. B 107, 115132 (2023)

[8] X. Turkeshi, PS, arXiv:2308.06321

The dynamics of interacting quantum many-body systems has two seemingly disparate but fundamental facets. The rst is the dynamics of real-space local observables, and if and how they thermalise. The second is to interpret the dynamics of the many-body state as that of a fictitious particle on the underlying Hilbert-space graph. In this work, we derive an explicit connection between these two aspects of the dynamics. We show that the temporal decay of the autocorrelation in a disordered quantum spin chain is explicitly encoded in how the return probability on Hilbert space approaches its late-time saturation. As such, the latter has the same functional form in time as the decay of autocorrelations but with renormalised parameters. Our analytical treatment is rooted in an understanding of the morphology of the time-evolving state on the Hilbert-space graph, and corroborated by exact numerical results.

Wednesday, 24 January 2024

In order to understand the nature of the transition between the MBL and ETH phases, I will use a series of approximations to develop RG flow equations based on the elimination and merging of nonperturbative regions. These equations resemble the Kosterlitz-Thouless (KT) flow equations, but there are important differences that place the MBL transition in a new universality class.

Quantum chaos can be diagnosed through the analysis of level statistics using the spectral form factor. This is the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole), when the system is chaotic. The spectral form factor captures both short- and long-range level correlations even in the presence of symmetries and it does not require unfolding. We discuss how this structure can be detected through the dynamics of two physical quantities accessible to experimental many-body quantum systems -- the survival probability and the spin autocorrelation function -- and how this manifestation of many-body quantum chaos implies relaxation times that grow exponentially with system size. However, quantities that exhibit the correlation hole are non-self-averaging. This means that the correlation hole is only visible after large averages over initial states or disorder realizations are performed, which is computationally and experimentally costly. We explain how self-averaging can be ensured by opening the system to an environment.

I shall discuss spectral correlations in many-body quantum mixtures of fermions, bosons, and qubits with periodically kicked spreading and mixing of species. We take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively, satisfying and breaking the conservation of a total number of species. We analytically derive the generating Hamiltonians whose spectral properties determine the spectral form factor in the leading order. We further analyze the system-size $(L)$ scaling of Thouless time $t^*$, beyond which the spectral form factor follows the prediction of random matrix theory. The $L$-dependence of $t^*$ crosses over from $\log L$ to $L^2$ with an increasing Jaynes-Cummings mixing between qubits and fermions or bosons in a finite-sized chain, and it finally settles to $t^*\propto \mathcal{O}(L^2)$ in the thermodynamic limit for any mixing strength. The Rabi mixing between qubits and fermions leads to $t^*\propto \mathcal{O}(\log L)$ , previously predicted for single species of qubits or fermions without total number conservation.

Understanding the dynamics of non-equilibrium quantum many-body systems is a central challenge in modern physics, with relevance across different branches of physics. As such, solvable models of quantum dynamics are valuable; but they are rare. In this talk, I will introduce a family of quantum circuits generated by the kicked Ising model in 1+1 dimensions which have interactions alternating between odd and even bonds in time, and prove that their entanglement dynamics can be analytically solved, yielding rich and varied phenomenology. Underpinning this solvability are the properties of global tri-unitary (three 'arrows of times'), as well as local "second-level dual-unitarity", a recently discovered property which constrains the behavior of pairs of local gates underlying the circuit under a space-time rotation. The phenomenology uncovered ranges from linear growth at half the maximal speed allowed by locality, followed by saturation to maximum entropy (i.e., thermalization to infinite temperature); to entanglement growth with saturation to extensive but sub-maximal entropy. We also find at certain special system parameters an apparently novel class of analytically-solvable dynamics which is non-chaotic, but neither integrable nor Clifford. Our findings extend our knowledge of interacting quantum systems whose thermalizing dynamics can be efficiently and analytically computed, going beyond the well-known examples of integrable models, Clifford circuits, and dual-unitary circuits.

I shall talk about our experimental system where we simultaneously cool and trap a large number of neutral Sodium and Potassium atoms. This machine is capable of investigating interesting physics relevant to quantum matter in and out of equilibrium. I shall discuss one particular example where we study spin noise spectroscopy in atomic systems with coherent two-photon Raman drive.

TBA

Chklovskii and Halperin theoretically predicted that a QPC between filling fractions ν=1 and 1/3 could act as a DC step-up transformer with an amplification factor of 3/2 which was observed recently in experiments. We revisit this problem in the context of AC transport in a bilayer quantum Hall (QH) setting. We show that the AC amplification is bounded by the DC limit of 3/2 in the presence of intra-layer electron-electron interactions alone, however, the possibility of having interlayer interactions open up a new avenue for amplification beyond the DC limit. This amplification can be understood in terms of displacement current due to the presence of ambient gate electrodes. We further show that AC conductance depicts resonances and anti-resonances resulting purely from interlayer interactions at certain magic frequencies.

We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to unitary circuit dynamics and focus on Floquet circuits arising as the Trotter decomposition of Hamiltonian dynamics. For short Trotter steps the results from Hamiltonian dynamics are recovered, whereas a large Trotter step results in different universal behavior characterized by the existence of local maximally ergodic operators: operators with vanishing autocorrelation functions, as exemplified in dual-unitary circuits. These two regimes are separated by a crossover in chaotic systems. Conversely, we find that free integrable systems exhibit a nonanalytic transition between these different regimes, where maximally ergodic operators appear at a critical Trotter step.

Thursday, 25 January 2024

Kicking a quantum system by subjecting it to a pulsed time-dependent Hamiltonian can give rise to a rich array of transport behaviors, from localization to thermalization to multifractality. I will describe two recent experiments on kicked quantum matter using ultracold neutral atoms. The first is an experimental observation of the “quantum boomerang effect,” a fundamental dynamical transport phenomenon unique to Anderson-localized matter which was only recently theoretically predicted and has not to our knowledge been previously observed. The second is an exploration of interaction-driven instabilities in an ensemble of quantum kicked rotors. The results provide experimental perspectives on a variety of phenomena ranging from quench dynamics to quantum chaos and thermalization.

I discuss three robust routes to ergodicity breaking in quantum dynamics: many body localization, fractonic symmetries, and higher form symmetries. I’ll explain how each of these works, their key properties, and degree of robustness.

Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly costly for today's noisy intermediate scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy. Classical adaptive solvers are well-developed to save numerical computation times. However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps. Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. The key conceptual element of our algorithm is a feedback loop which self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth. It even allows for a controlled asymptotic long-time error, where usual Trotterized dynamics is facing difficulties. Another key advantage of our quantum algorithm is that any desired conservation law can be included in the self-correcting feedback loop, which has potentially a wide range of applicability. We demonstrate the capabilities by enforcing gauge invariance which is crucial for a faithful and long-sought quantum simulation of lattice gauge theories. Our algorithm can be potentially useful on a more general level whenever time discretization is involved concerning, for instance, also numerical approaches based on time-evolving block decimation methods.

References: [1] PRX Quantum 4, 030319 (2023);

[2] arXiv:2307.10327 (2023)

Quantum mechanics is ruled by Hermitian generators inducing unitary propagation, nevertheless, when tracing out some degrees of freedom one can end up with non-Hermitian operators. An example is entanglement or out-of-time-ordered correlation functions in random circuits, where the relaxation dynamics is described by a non-Hermitian Markovian matrix with a finite spectral gap. Naturally one would expect that the relaxation, i.e., the rate of generating entanglement, will be given by this finite gap. However, this is not the case. Rather, in the thermodynamic limit the rate is given by a phantom eigenvalue -- an "eigenvalue" that is not in the spectrum. Resolution of this puzzle will lead to a pseudospectrum and a realization that when dealing with non-Hermitian matrices being exact can actually be wrong, while being slightly wrong is correct.

We study the localisation-delocalisation transition (i.e. the Many-Body localisation transition) of a system of one dimensional interacting fermions with random disorder in Fock space. We do this by adapting a recursive real method to calculate the Green's function in Fock space. The imaginary part of the self-energy thus obtained can be employed as an order parameter for the transition. A calculation of this quantity reveals a diverging "non-ergodic" Fock space volume with an essential singularity as the transition is approached from the delocalized side and a diverging localization length with a critical exponent when the approach is from the localized side. We compare the results for the disordered system to those for a system with a quasiperiodic potential and show that sample to sample fluctuations of the self-energy can distinguish between the two types of systems.

Quantum critical engines, i.e., quantum engines operating close to quantum phase transitions, show universal features in their output, following the Kibble-Zurek mechanism. I will discuss universality in the work output of finite-time quantum critical engines, operating at finite temperatures.

Here we will discuss how approximate but perpetual conservation laws emerge in generic periodically driven many-body quantum systems. These conservation laws puts up strong constraints that prevent the system from themalizing. This provides an example of ergodicity breaking due to fragmentation of the Hilbert space into the degenerate subspaces of the conserved quantities. We will demonstrate the stability of these conservation laws in the thermodynamic limit using numerical simulations of infinite systems.