Two-step relaxation in local many-body Floquet systems

Abstract

We want to understand how relaxation process from an initial non-generic state proceeds towards a long-time typical state reached under unitary quantum evolution. One would expect that after some initial correlation time relaxation will be a simple exponential decay with constant decay rate. We show that this is not necessarily the case. Studying various Floquet systems with fixed two-qubit gates, and focusing on purity and out-of-time-ordered correlation functions, we find that in many situations relaxation proceeds in two phases of exponential decay having different relaxation rates. Namely, in the thermodynamic limit the relaxation rate exhibits a change at a critical time proportional to system's size. The initial thermodynamically relevant rate can be slower or faster than the asymptotic one, demonstrating that the recently discovered phantom relaxation, in which the decay is slower than predicted by a nonzero transfer matrix gap, is not limited to only random circuits.

8 pages; v2: 9 pages

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Aspects of generic entanglement
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Statistical distribution of quantum entanglement for a random bipartite state
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Quantum and classical Floquet prethermalization
• Entanglement of random vectors
• Lower bounds on the complexity of simulating quantum gates
• Growth of entanglement of generic states under dual-unitary dynamics
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Purity decay rate in random circuits with different configurations of gates

Cited by in corpus (4)

• Unraveling the emergence of quantum state designs in systems with symmetry
• Theory of Irreversibility in Quantum Many-Body Systems
• Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution
• Boom and bust cycles due to pseudospectra of matrices with unimodular spectra