Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits

TL;DR

This paper investigates the spectral properties of diffusive magnetization transport in U(1)-invariant qubit circuits, revealing how Ruelle-Pollicott resonances encode diffusion and decay behaviors, and proposing a continuum of eigenvalues affecting non-exponential decay.

Contribution

It introduces a spectral analysis framework for magnetization-conserving qubit circuits, linking Ruelle-Pollicott resonances to diffusion constants and decay phenomena, with a conjecture on a continuum of eigenvalues.

Findings

Diffusive transport reflected in Gaussian k dependence of leading eigenvalue.

Extraction of diffusion constant from the spectrum.

Existence of a continuum of eigenvalues below the diffusive resonance.

Abstract

We study Ruelle-Pollicott resonances of translationally invariant magnetization-conserving qubit circuits via the spectrum of the quasi-momentum-resolved truncated propagator of extensive observables. Diffusive transport of the conserved magnetization is reflected in the Gaussian quasi-momentum $k$ dependence of the leading eigenvalue (Ruelle-Pollicott resonance) of the truncated propagator for small $k$. This, in particular, allows us to extract the diffusion constant. For large $k$, the leading Ruelle-Pollicott resonance is not related to transport and governs the exponential decay of correlation functions. Additionally, we conjecture the existence of a continuum of eigenvalues below the leading diffusive resonance, which governs non-exponential decay, for instance, power-law hydrodynamic tails. We expect our conclusions to hold for generic systems with exactly one U(1) conserved quantity.