Long tail distributions near the many body localization transition

TL;DR

This paper investigates the behavior of eigenstates and entanglement entropy distributions near the many-body localization transition in a disordered quantum spin chain, revealing the breakdown of ETH and the emergence of rare states and long-tailed distributions.

Contribution

It provides evidence for ETH breakdown and rare states near the transition, linking localized boundary regions to subdiffusive transport mechanisms.

Findings

ETH holds in the thermal phase but breaks down in the localized phase.

Rare states without ETH become more frequent near the transition.

Entanglement entropy distribution develops long tails down to zero near the transition.

Abstract

The random field S=1/2 Heisenberg chain exhibits a dynamical many body localization transition at a critical disorder strength, which depends on the energy density. At weak disorder, the eigenstate thermalization hypothesis (ETH) is fulfilled on average, making local observables smooth functions of energy, whose eigenstate-to-eigenstate fluctuations decrease exponentially with system size. We demonstrate the validity of ETH in the thermal phase as well as its breakdown in the localized phase and show that rare states exist which do not strictly follow ETH, becoming more frequent closer to the transition. Similarly, the probability distribution of the entanglement entropy at intermediate disorder develops long tails all the way down to zero entanglement. We propose that these low entanglement tails stem from localized regions at the subsystem boundaries which were recently discussed as a possible mechanism for subdiffusive transport in the ergodic phase.