The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains

TL;DR

This paper investigates whether constrained Hilbert spaces, exemplified by a Fibonacci anyon chain, allow for local thermalization and the eigenstate thermalization hypothesis (ETH), demonstrating that ETH can hold despite the constraints.

Contribution

The study provides numerical evidence that ETH applies in constrained Hilbert spaces of non-Abelian anyon chains, showing constraints do not prevent thermalization.

Findings

ETH holds for local observables in the constrained Hilbert space

Influence of measurements decays exponentially, indicating locality

Certain non-local observables also obey ETH

Abstract

Many phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this article, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality, by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free non-integrable model. We also find that certain non-local observables obey ETH.