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

Understand

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.