Many-body localization beyond eigenstates in all dimensions

TL;DR

This paper challenges the conventional understanding of many-body localization (MBL) by showing that systems can exhibit thermal eigenstate properties despite being localized, especially in higher dimensions, due to boundary effects and localized conserved operators.

Contribution

It introduces the concept of localized approximately conserved operators (l*-bits) and demonstrates their role in MBL, revealing new phenomena like eigenstate phase transitions and thermal eigenstates in higher dimensions.

Findings

MBL systems can have thermal eigenstates despite localization.

l*-bits underpin localization and can cause eigenstate phase transitions.

Boundary effects destabilize MBL in dimensions greater than one.

Abstract

Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators (l$^*$-bits) underlie localization in such systems. In dimensions $d>1$, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to l$^*$-bits. Physical consequences of l$^*$-bits include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in $d=1$ and thermal eigenstates at all parameters in $d>1$. Near-term experiments in ultra-cold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of l$^*$-bits.