Many-body delocalisation as symmetry breaking

TL;DR

This paper proposes a framework where the transition from many-body localized to ergodic phases is understood as a symmetry-breaking phenomenon, using spectral form factors and transfer matrices in Floquet spin chains.

Contribution

It introduces a novel symmetry-breaking perspective on the MBL transition, identifying a local order parameter and analyzing spectral form factors via transfer matrices.

Findings

In the MBL phase, the transfer matrix has a unique leading eigenvalue.

In the ergodic phase, the leading eigenvalues become degenerate, indicating symmetry breaking.

Long-range correlations are present only in the ergodic phase.

Abstract

We present a framework in which the transition between a many-body localised (MBL) phase and an ergodic one is symmetry breaking. We consider random Floquet spin chains, expressing their averaged spectral form factor (SFF) as a function of time in terms of a transfer matrix that acts in the space direction. The SFF is determined by the leading eigenvalues of this transfer matrix. In the MBL phase the leading eigenvalue is unique, as in a symmetry-unbroken phase, while in the ergodic phase and at late times the leading eigenvalues are asymptotically degenerate, as in a system with degenerate symmetry-breaking phases. We identify the broken symmetry of the transfer matrix, introduce a local order parameter for the transition, and show that the associated correlation functions are long-ranged only in the ergodic phase.