Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems

TL;DR

This paper investigates momentum-dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems, revealing how correlation decay rates vary with symmetry and identifying regimes with distinct decay behaviors.

Contribution

It introduces a momentum-resolved spectral analysis of quantum many-body systems and predicts the structure of the spectrum, including annular rings and isolated resonances, in the kicked Ising model.

Findings

Correlation functions decay at different rates depending on their symmetries.

Identifies a mixing regime with power-law decay of correlations.

Proposes an exact expression for the singular values of the operator propagator.

Abstract

We study Ruelle-Pollicott resonances in translationally invariant quantum many-body lattice systems via spectra of a momentum-resolved operator propagator on infinite systems. Momentum dependence gives insight into the decay of correlation functions, showing that, depending on their symmetries, different correlation functions in general decay with different rates. Focusing on the kicked Ising model the spectrum seems to be typically composed of an annular random matrix like ring whose size we theoretically predict, and few isolated resonances. We identify several interesting regimes, including a mixing regime with a power-law decay of correlation functions. In that regime we also observe a huge difference in time-scales of different correlation functions due to an almost conserved operator. An exact expression for the singular values of the operator propagator is conjectured, showing that it becomes singular at a special point.