Renormalization view on resonance proliferation between many-body localized phases

TL;DR

This paper investigates how many-body resonances affect the stability of many-body localized phases and topological order, revealing resonance proliferation near phase transitions that may lead to ergodic behavior.

Contribution

It introduces a Clifford circuit-based real space renormalization group method to analyze resonance properties in disordered interacting systems with topological order.

Findings

MBL phases remain stable to resonances away from transition

Resonance proliferation destabilizes localization near phase transition

Evidence of an intervening ergodic phase due to avalanche instability

Abstract

Topology and many-body localization (MBL) have opened new avenues for preserving quantum information at finite energy density. Resonant delocalization plays a crucial role in destabilizing these phenomena. In this work, we study the statistical properties of many-body resonances in a disordered interacting Ising model - which can host symmetry protected topological order - using a Clifford circuit encoding of the real space renormalization group which allows the resonant properties of the wave functions to be efficiently characterized. Our findings show that both the trivial and topologically ordered MBL phases remain stable to the resonances, but in the vicinity of the transition between them localization is destabilized by resonance proliferation. Diverging susceptibility towards the development of an avalanche instability suggests an intervening ergodic phase. We are also able to access the local integrals of motion in the MBL phases and identify the topological edge-mode operators in the ordered phase. Our results have important implications for the stability of MBL and phase transitions between distinct MBL phases with and without symmetries.