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David Logan (University of Oxford & Indian Institute of Science, Bangalore)
Date & Time
Tue, 14 May 2019, 15:00 to 16:00
Feynman Lecture Hall, ICTS Campus Bangalore

Classical percolation models in Fock space are constructed and studied, as proxies for the quantum many-body localisation transition. Percolation rules are defined for two models of disordered quantum spin-chains, using their microscopic  quantum Hamiltonians and the topologies of the associated Fock- space graphs. The existence of the percolation transition, and its critical properties, are deduced in  several ways:  exact solution for the critical disorder and correlation length exponent, systematic numerical study of the statistics and scaling of Fock- space clusters, and physical arguments based on freezing of local real-space segments of spins. Local observables averaged over Fock-space clusters are also shown to carry signatures of the transition, with their behaviour in direct analogy to that of corresponding eigenstate expectation values across the MBL transition. Fock-space clusters can likewise be explored under a mapping to kinetically constrained models;  dynamics within this framework also show the ergodicity-breaking transition, and permit access to system sizes some two orders of magnitude larger than those possible for exact enumeration.