Numerical evidence for the non-Abelian eigenstate thermalization hypothesis

TL;DR

This paper provides numerical and analytical evidence supporting a non-Abelian eigenstate thermalization hypothesis in quantum many-body systems, demonstrating its validity in a 1D Heisenberg chain with noncommuting conserved quantities.

Contribution

It numerically supports the non-Abelian ETH in a 1D Heisenberg model and proves its self-consistency, advancing understanding of thermalization with non-Abelian symmetries.

Findings

Numerical results align with seven predictions of the non-Abelian ETH.

Analytical proof confirms the self-consistency of the non-Abelian ETH.

Supports the application of non-Abelian ETH in quantum thermodynamics.

Abstract

The eigenstate thermalization hypothesis (ETH) explains how generic quantum many-body systems thermalize internally. It implies that local operators' time-averaged expectation values approximately equal their thermal expectation values, regardless of microscopic details. The ETH's range of applicability therefore impacts theory and experiments. Murthy $\textit{et al.}$ recently showed that non-Abelian symmetries conflict with the ETH. Such symmetries have excited interest in quantum thermodynamics lately, as they are equivalent to conserved quantities that fail to commute with each other and noncommutation is a quintessentially quantum phenomenon. Murthy $\textit{et al.}$ proposed a non-Abelian ETH, which we support numerically. The numerics model a one-dimensional (1D) next-nearest-neighbor Heisenberg chain of up to 18 qubits. We represent local operators with matrices relative to an energy eigenbasis. The matrices bear out seven predictions of the non-Abelian ETH. We also prove analytically that the non-Abelian ETH exhibits a self-consistency property. The proof relies on a thermodynamic-entropy definition different from that in Murthy $\textit{et al.}$ This work initiates the observation and application of the non-Abelian ETH.