Off-diagonal matrix elements of local operators in many-body quantum systems
arXiv:1407.2043 · doi:10.1103/PhysRevE.91.012144
Abstract
In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the eigenstates of the system. The temporal fluctuations around this value, response to further perturbations, and the relaxation toward this asymptotic value, are all determined by the off-diagonal matrix elements. Motivated by this non-equilibrium role, we present generic statistical properties of off-diagonal matrix elements of local observables in two families of interacting many-body systems with local interactions. Since integrability (or lack thereof) is an important ingredient in the relaxation process, we analyze models that can be continuously tuned to integrability. We show that, for generic non-integrable systems, the distribution of off-diagonal matrix elements is a gaussian centered at zero. As one approaches integrability, the peak around zero becomes sharper, so that the distribution is approximately a combination of two gaussians. We characterize the proximity to integrability through the deviation of this distribution from a gaussian shape. We also determine the scaling dependence on system size of the average magnitude of off-diagonal matrix elements.
10 pages, 6 figures
References in corpus (25)
- Thermalization and its mechanism for generic isolated quantum systems
- Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
- Breakdown of thermalization in finite one-dimensional systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Interaction Quench in the Hubbard model
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- Dephasing and the steady state in quantum many-particle systems
- Strong and weak thermalization of infinite non-integrable quantum systems
- Generalized Thermalization in an Integrable Lattice System
- Quantum quench dynamics of the Luttinger model
- Nonthermal steady states after an interaction quench in the Falicov-Kimball model
- Eigenstate thermalization within isolated spin-chain systems
- Quantum Quenches, Thermalization and Many-Body Localization
- Quantum chaos and thermalization in gapped systems
- Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
- Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
- Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
- Finite-size corrections vs. relaxation after a sudden quench
- Relevance of the eigenstate thermalization hypothesis for thermal relaxation
- Initial state dependence of the quench dynamics in integrable quantum systems. II. Thermal states
- Relaxation and Thermalization after a Quantum Quench: Why Localization is Important
- Relaxation Dynamics of Disordered Spin Chains: Localization and the Existence of a Stationary State
- Gaussian Equilibration
- Quantum quench dynamics of the Bose-Hubbard model at finite temperatures
- Macroscopically deterministic, Markovian thermalization in finite quantum spin systems
Cited by in corpus (4)
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
- Quantum quenches and many-body localization in the thermodynamic limit
- Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements