Probing thermalization through spectral analysis with matrix product operators

TL;DR

This paper introduces a spectral analysis method combining matrix product operators and Chebyshev expansions to study thermalization in quantum many-body systems without explicit time evolution simulations.

Contribution

It presents a novel approach that efficiently probes spectral properties and thermalization in large quantum spin chains using matrix product operators and polynomial expansions.

Findings

Confirmed thermalization in non-integrable Ising chain for multiple initial states

Demonstrated ability to analyze large systems beyond traditional simulation limits

Provided detailed spectral densities for spin chain models

Abstract

We combine matrix product operator techniques with Chebyshev polynomial expansions and present a method that is able to explore spectral properties of quantum many-body Hamiltonians. In particular, we show how this method can be used to probe thermalization of large spin chains without explicitly simulating their time evolution, as well as to compute full and local densities of states. The performance is illustrated with the examples of the Ising and PXP spin chains. For the non-integrable Ising chain, our findings corroborate the presence of thermalization for several initial states, well beyond what direct time-dependent simulations have been able to achieve so far.