Particle-hole symmetry, many-body localization, and topological edge modes

TL;DR

This paper investigates how interactions influence the excited states of disordered one-dimensional fermionic systems, revealing that even weak interactions can lead to thermalization or symmetry breaking, disrupting quantum criticality and topological order.

Contribution

It demonstrates that interactions, though irrelevant in the ground state, significantly alter the structure of excited states, affecting localization and symmetry properties in disordered systems.

Findings

Interactions cause degeneracy splitting, leading to thermalization or spin glass phases.

Edges of the spectrum are less localized than the center.

Certain excited state topological orders are ruled out by these results.

Abstract

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders.