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

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.

21 + 12 pages, improved numerics and presentation

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• Subexponential decay of local correlations from diffusion-limited dephasing
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems