Unitary equilibration after a quantum quench of a thermal state

Abstract

In this work we investigate the equilibration dynamics after a sudden Hamiltonian quench of a quantum spin system initially prepared in a thermal state. To characterize the equilibration we evaluate the Loschmidt echo, a global measure for the degree of distinguishability between the initial and time-evolved quenched states. We present general results valid for small quenches and detailed analysis of the quantum XY chain. The result is that quantum criticality manifests, even at small but finite temperatures, in a universal double-peaked form of the echo statistics and poor equilibration for sufficiently relevant perturbations. In addition, for this model we find a tight lower bound on the Loschmidt echo in terms of the purity of the initial state and the more-easily-evaluated Hilbert-Schmidt inner product between initial and time-evolved quenched states. This bound allows us to relate the time-averaged Loschmidt echo with the purity of the time-averaged state, a quantity that has been shown to provide an upper bound on the variance of observables.

13 pages, 4 figures

References in corpus (21)

• Dynamics of Loschmidt echoes and fidelity decay
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
• Quantum critical scaling of the geometric tensors
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Strongly correlated fermions after a quantum quench
• Absence of Thermalization in Nonintegrable Systems
• Typicality for Generalized Microcanonical Ensembles
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Quench dynamics near a quantum critical point
• Mixed-state fidelity and quantum criticality at finite temperature
• Decoherence induced by interacting quantum spin baths
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Bures metric over thermal state manifolds and quantum criticality
• Unitary equilibrations: probability distribution of the Loschmidt echo
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• Quench dynamics near a quantum critical point: application to the sine-Gordon model
• Universal equilibrium distribution after a small quantum quench
• Decoherence by engineered quantum baths
• Quantum quench dynamics of the Bose-Hubbard model at finite temperatures
• The transition to chaos of coupled oscillators: An operator fidelity susceptibility study

Cited by in corpus (16)

• Disentangling dynamical phase transitions from equilibrium phase transitions
• Equilibration of isolated macroscopic quantum systems
• Relaxation timescales and decay of correlations in a long-range interacting quantum simulator
• Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Quench echo and work statistics in integrable quantum field theories
• Quantum Phase Transition in a Quantum Ising Chain at Nonzero Temperatures
• Quantum quench in the Luttinger model with finite temperature initial state
• Exact work statistics of quantum quenches in the anisotropic XY model
• The approach to typicality in many-body quantum systems
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Detection of quantum phase boundary at finite temperatures in integrable spin models
• Probing the superfluid-insulator phase transition by a non-Hermitian external field
• Quantum quenches of ion Coulomb crystals across structural instabilities II: thermal effects
• Signature of quantum phase transition manifested in quantum fidelity at finite temperature
• Nonlocal pseudospin dynamics in a quantum Ising chain