Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
arXiv:2008.03745 · doi:10.1103/PhysRevResearch.2.033210
Abstract
We investigate how the observable relaxation behavior of an isolated quantum many-body system is modified in response to weak-to-moderate perturbations within a nonperturbative typicality framework. A key role is played by the so-called perturbation profile, which characterizes the dependence of the perturbation matrix elements in the eigenbasis of the unperturbed Hamiltonian on the difference of the corresponding energy eigenvalues. In particular, a banded matrix structure is quantitatively captured by a perturbation profile which approaches zero for large energy differences. The temporal modification of the relaxation is linked to the perturbation profile via a nonlinear integral equation, which admits approximate analytical solutions for sufficiently weak and strong perturbations, and for which we work out a numerical solution scheme in the general case. As an example, we consider a spin lattice model with a pronounced banded matrix structure, and we find very good agreement of the numerics with our analytical predictions without any free fit parameter.
arXiv comment13 pages, 4 figures
References in corpus (39)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Statistics of energy levels and eigenfunctions in disordered systems
- Generalized Gibbs ensemble in integrable lattice models
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Dynamics of Loschmidt echoes and fidelity decay
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Prethermalization
- Interaction Quench in the Hubbard model
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems
- Quantum quench dynamics
- Prethermalization and universal dynamics in near-integrable quantum systems
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates
- Dynamical typicality of quantum expectation values
- Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
- Prethermalization and Thermalization in Isolated Quantum Systems
- Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- Quench Dynamics of Isolated Many-Body Quantum Systems
- Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements
- The adiabatic theorem and linear response theory for extended quantum systems
- Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
- Dynamical typicality of isolated many-body quantum systems
- Thermalisation of Local Observables in Small Hubbard Lattices
- Relaxation theory for perturbed many-body quantum systems versus numerics and experiment
- Off-Diagonal Observable Elements from Random Matrix Theory: Distributions, Fluctuations, and Eigenstate Thermalization
- Typicality of Prethermalization
- Atypicality of Most Few-Body Observables
- Impact of eigenstate thermalization on the route to equilibrium
- Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements
- Generalized quantum microcanonical ensemble from random matrix product states
- A Selective Relaxation Method for Numerical Solution of Schrödinger Problems
- Modelling equilibration of local many-body quantum systems by random graph ensembles
- Predicting Imperfect Echo Dynamics in Many-Body Quantum Systems
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