Particle fluctuations and the failure of simple effective models for many-body localized phases

TL;DR

This paper shows that simple effective models fail to capture particle fluctuations in the many-body localized phase, suggesting that more complex interactions are essential for understanding localization.

Contribution

It demonstrates that effective models ignoring assisted and pair hopping terms cannot explain observed particle fluctuations in the MBL phase.

Findings

Simple effective models are insufficient for MBL particle fluctuations.

Assisted and pair hopping terms are crucial in the microscopic Hamiltonian.

Existence of exponentially many conserved local charges in MBL is questionable.

Abstract

We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case (Anderson localization) and in effective models where only interaction terms diagonal in the Anderson basis are kept. We demonstrate that these types of simple effective models cannot account for the particle number fluctuations observed in the MBL phase of the microscopic model. This implies that assisted and pair hopping terms---generated when transforming the microscopic Hamiltonian into the Anderson basis---cannot be neglected. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved local charges. If such exactly conserved local charges do not exist, then particles are expected to ultimately delocalize for any finite disorder strength.