The approach to typicality in many-body quantum systems

Abstract

The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization. Here we give numerical evidence that many-body lattice systems generically approach typicality as the number of subsystems is increased, and thus provide further support for the eigenstate thermalization hypothesis. Our results indicate that the deviation of many-body systems from typicality decreases exponentially with the number of systems. Further, by averaging over a number of randomly-selected nearest-neighbor interactions, we obtain a power-law for the atypicality as a function of the Hilbert space dimension, distinct from the power-law possessed by random Hamiltonians.

6 pages, 2 png figures, revtex4

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• Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
• Macroscopically deterministic, Markovian thermalization in finite quantum spin systems
• Onset of Fokker-Planck dynamics within a Closed Finite Spin System
• Statistical description of small quantum systems beyond weak-coupling limit
• Coherence generation, symmetry algebras and Hilbert space fragmentation
• Initial State Independent Equilibration at the Breakdown of the Eigenstate Thermalization Hypothesis
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Quantum reservoir computing for predicting and characterizing chaotic maps