Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
arXiv:1901.02119 · doi:10.1103/PhysRevE.99.042116
Abstract
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution in each of these classes agrees with that of random matrices with the corresponding symmetry. By investigating the ratios between the standard deviations of diagonal and off-diagonal matrix elements, we numerically find that they become universal, depending only on symmetries of the Hamiltonian and an observable, as predicted by random matrix theory. These universal ratios are evaluated from long-time dynamics of small isolated quantum systems.
arXiv comment14 pages, 8 figures; published version
References in corpus (50)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Random Matrix Theories in Quantum Physics: Common Concepts
- Black holes and the butterfly effect
- The many-body localization phase transition
- Measuring entanglement entropy through the interference of quantum many-body twins
- Quantum thermalization through entanglement in an isolated many-body system
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Many-body localization in a quantum simulator with programmable random disorder
- Chaos in quantum channels
- The approach to thermal equilibrium in quantized chaotic systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Strong and weak thermalization of infinite non-integrable quantum systems
- Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Random Matrices and Chaos in Nuclear Physics
- Semiclassical Foundation of Universality in Quantum Chaos
- Finite-size scaling of eigenstate thermalization
- Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
- Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
- Spectral statistics in spatially extended chaotic quantum many-body systems
- Spectral statistics across the many-body localization transition
- Anomalous thermalization in ergodic systems
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Eigenstate thermalization within isolated spin-chain systems
- Many-body quantum chaos: Analytic connection to random matrix theory
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- Typical fast thermalization processes in closed many-body systems
- Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
- Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
- Time-resolved observation of thermalization in an isolated quantum system
- Phase Transition in the Density of States of Quantum Spin Glasses
- Entanglement, avoided crossings and quantum chaos in an Ising model with a tilted magnetic field
- Joint probability densities of level spacing ratios in random matrices
- Eigenstate Thermalization, Random Matrix Theory and Behemoths
- Entangling power of time-evolution operators in integrable and nonintegrable many-body systems
- Slowest local operators in quantum spin chains
- Relevance of the eigenstate thermalization hypothesis for thermal relaxation
- Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?
- Thermalization of entanglement
- Atypicality of Most Few-Body Observables
- Local entanglement structure across a many-body localization transition
- Canonical Universality
- Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
- Irreversible dynamics in quantum many-body systems
- Density and spacings for the energy levels of quadratic Fermi operators
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