Certain General Constraints on the Many-Body Localization Transition

TL;DR

This paper uses entanglement entropy properties to constrain the nature of the many-body localization transition, showing that certain types of continuous transitions must involve thermal critical states, while others involve non-ergodic delocalized phases.

Contribution

It provides theoretical constraints on the possible characteristics of the many-body localization transition using entanglement entropy inequalities.

Findings

Critical eigenstates are necessarily thermal at continuous MBL transitions.

Thermal entropy equals critical entanglement entropy at the transition.

Non-ergodic delocalized phase has volume law entanglement entropy tending to zero near transition.

Abstract

Isolated quantum systems at strong disorder can display many-body localization (MBL), a remarkable phenomena characterized by an absence of conduction even at finite temperatures. As the ratio of interactions to disorder is increased, one expects that an MBL phase will eventually undergo a dynamical phase transition to a delocalized phase. Here we constrain the nature of such a transition by exploiting the strong subadditivity of entanglement entropy, as applied to the many-body eigenstates close to the transition in general dimensions. In particular, we show that at a putative continuous transition between an MBL and an ergodic delocalized phase, the critical eigenstates are necessarily thermal, and therefore, the critical entanglement entropy equals the thermal entropy. We also explore a qualitatively different continuous localization-delocalization transition, where the delocalized phase is non-ergodic whose volume law entanglement entropy tends to zero as the transition is approached.