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

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.

v1: 12 pages; v2: 14p., new Fig.12 explaining prethermalization plateau in the mixing regime

References in corpus (6)

• An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications
• Chaos and Complexity of quantum motion
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Leading Pollicott-Ruelle Resonances for Chaotic Area-Preserving Maps
• Classical approach to equilibrium of out-of-time ordered correlators in mixed systems

Cited by in corpus (17)

• Pseudomode expansion of many-body correlation functions
• Theory of Irreversibility in Quantum Many-Body Systems
• Integrability is generic in homogeneous U(1)-invariant nearest-neighbor qubit circuits
• Ringdown in the SYK model
• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits
• Opening Krylov space to access all-time dynamics via dynamical symmetries
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit
• Subexponential decay of local correlations from diffusion-limited dephasing
• Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Symmetry Properties of Quantum Dynamical Entropy
• Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Error bounds on the universal Lindblad equation in the thermodynamic limit
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap