26 February 2021

A recent publication based on the work done by ICTS post-doctoral fellow Dr. Abhishodh Prakash and ICTS faculty member Dr. Manas Kulkarni (in collaboration with Dr. J. H. Pixley from Rutgers University, USA), titled ‘Universal spectral form factor for many-body localization’, in the journal Physical Review Research (Letter), has been selected by the Editors as an ‘Editors’ Suggestion’.

Universality has long been a powerful guiding principle that has facilitated tremendous progress in understanding equilibrium phases and phenomena. At the most practical level, it allows one to substitute complicated models of physical systems of interest with simpler ones that are tractable. The culmination of decades of work has started to reveal that such a notion of universality might also be present for systems exhibiting quantum chaos, which are believed to constitute a non-equilibrium 'eigenstate phase' of matter. This universality is observed by studying correlations present in the spectrum of energies which are reproduced by a remarkably simpler system - random matrix ensembles! 

Many-body-localized (MBL) systems, which have properties in complete contrast to quantum chaotic ones, are believed to form another eigenstate phase. However, unlike quantum chaotic systems, universal signatures for the MBL phase have, so far, not been identified beyond the absence of local level repulsion. In this paper, using an exact formula they obtain for Poisson numbers which mimic MBL energies, the authors predict the existence of a ‘power-law regime’ in the spectral form factor (a quantity which measures correlations in the energy spectrum) where chaotic systems exhibit a universal `ramp'. These theoretical predictions are checked numerically on models that are known to exhibit MBL and an excellent agreement is found thus supporting that MBL is indeed a robust phase with its own unique universal signatures

This study marks a potentially significant step forward in the study of many-body-localization and was selected by the Editors due to its particular interest, importance and clarity.