Kubo-Martin-Schwinger relation for energy eigenstates of SU(2)-symmetric quantum many-body systems

TL;DR

This paper derives a KMS relation for energy eigenstates in SU(2)-symmetric quantum many-body systems, extending thermodynamic understanding to systems with non-Abelian symmetries and supporting findings with numerical simulations.

Contribution

It introduces a KMS relation for SU(2)-symmetric systems' eigenstates using a non-Abelian ETH, revealing larger finite-size corrections and broadening thermodynamics in quantum physics.

Findings

Finite-size correction scales as inverse system size or polynomially larger.

Numerical simulations of a Heisenberg chain support the theoretical correction scaling.

The work extends thermodynamic principles to systems with non-Abelian symmetries.

Abstract

The fluctuation-dissipation theorem (FDT) is a fundamental result in statistical mechanics. It stipulates that, if perturbed out of equilibrium, a system responds at a rate proportional to a thermal-equilibrium property. Applications range from particle diffusion to electrical-circuit noise. To prove the FDT, one must prove that common thermal states obey a symmetry property, the Kubo-Martin-Schwinger (KMS) relation. Energy eigenstates of certain quantum many-body systems were recently proved to obey the KMS relation. The proof relies on the eigenstate thermalization hypothesis (ETH), which explains how such systems thermalize internally. This KMS relation contains a finite-size correction that scales as the inverse system size. Non-Abelian symmetries conflict with the ETH, so a non-Abelian ETH was proposed recently. Using it, we derive a KMS relation for SU(2)-symmetric quantum many-body systems' energy eigenstates. The finite-size correction scales as usual under certain circumstances but can be polynomially larger in others, we argue. We support the ordinary-scaling result numerically, simulating a Heisenberg chain of 16-24 qubits. The numerics, limited by computational capacity, indirectly support the larger correction. This work helps extend into nonequilibrium physics the effort, recently of interest across quantum physics, to identify how non-Abelian symmetries may alter conventional thermodynamics.