Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems
arXiv:2004.03917 · doi:10.1103/PhysRevLett.125.050603
Abstract
The fluctuation dissipation theorem~(FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address the question whether the FDT is obeyed by isolated quantum systems in an energy eigenstate. In the framework of the eigenstate thermalization hypothesis, we derive the formal expression for two-time correlation functions in the energy eigenstates or in the diagonal ensemble. They satisfy the Kubo-Martin-Schwinger condition, which is the sufficient and necessary condition for the FDT, in the infinite system size limit. We also obtain the finite size correction to the FDT for finite-sized systems. With extensive numerical works for the XXZ spin chain model, we confirm our theory for the FDT and the finite size correction. Our results can serve as a guide line for an experimental study of the FDT on a finite-sized system.
12 pages with revised figures
References in corpus (10)
- Thermalization and its mechanism for generic isolated quantum systems
- Experimental Observation of a Generalized Gibbs Ensemble
- Breakdown of thermalization in finite one-dimensional systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Dynamical Correlations after a Quantum Quench
- Eigenstate thermalization within isolated spin-chain systems
- Entanglement and matrix elements of observables in interacting integrable systems
- Guide to Exact Diagonalization Study of Quantum Thermalization
- Joule expansion of a pure many-body state
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- Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations
- Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
- Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
- Quantum master equation from the eigenstate thermalization hypothesis
- Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
- Out-of-equilibrium Eigenstate Thermalization Hypothesis
- Numerical evidence for the non-Abelian eigenstate thermalization hypothesis