Spectral tensor networks for many-body localization

TL;DR

This paper introduces a spectral tensor network framework that efficiently represents the entire energy spectrum of many-body localized systems, enabling practical computation of expectation values in eigenstates.

Contribution

It proposes a novel tensor network approach for representing the eigenspectra of MBL systems based on local integrals of motion, with rigorous results for idealized models.

Findings

Efficient spectral tensor network representation for MBL systems.

Allows computation of expectation values in eigenstates.

Rigorous results for systems with finite support integrals of motion.

Abstract

Subsystems of strongly disordered, interacting quantum systems can fail to thermalize because of the phenomenon of many-body localization (MBL). In this article, we explore a tensor network description of the eigenspectra of such systems. Specifically, we will argue that the presence of a complete set of local integrals of motion in MBL implies an efficient representation of the entire spectrum of energy eigenstates with a single tensor network, a \emph{spectral} tensor network. Our results are rigorous for a class of idealized systems related to MBL with integrals of motion of finite support. In one spatial dimension, the spectral tensor network allows for the efficient computation of expectation values of a large class of operators (including local operators and string operators) in individual energy eigenstates and in ensembles.