Bounds on chaos from the eigenstate thermalization hypothesis
arXiv:1906.10808 · doi:10.1103/PhysRevLett.123.230606
Abstract
We show that the known bound on the growth rate of the out-of-time-order four-point correlator in chaotic many-body quantum systems follows directly from the general structure of operator matrix elements in systems that obey the eigenstate thermalization hypothesis. This ties together two key paradigms of thermal behavior in isolated many-body quantum systems.
arXiv comment4 pages, 0 figures. Revised in response to reviewer comments (results unchanged, but expanded and clarified discussion of several points). Accepted for publication in Physical Review Letters
References in corpus (16)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Black holes and the butterfly effect
- The approach to thermal equilibrium in quantized chaotic systems
- Two-dimensional conformal field theory and the butterfly effect
- A Universal Operator Growth Hypothesis
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Correlations in Chaotic Eigenfunctions at Large Separation
- Wave function correlations on the ballistic scale: Exploring quantum chaos by quantum disorder
- Random Matrix Elements and Eigenfunctions in Chaotic Systems
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