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Subsystem eigenstate thermalization hypothesis.

Anatoly Dymarsky1,2, Nima Lashkari3, Hong Liu3

  • 1Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.

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We introduce subsystem ETH, a new formulation of the eigenstate thermalization hypothesis for chaotic quantum systems. This approach uses subsystem reduced density matrices to define thermalization for specific observables, supported by Ising spin chain simulations.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • The eigenstate thermalization hypothesis (ETH) explains how isolated quantum systems reach thermal equilibrium.
  • Canonical typicality provides a qualitative understanding of thermalization in chaotic quantum systems.

Purpose of the Study:

  • To propose a refined formulation of the ETH, termed subsystem ETH, applicable to chaotic quantum systems.
  • To define the conditions under which thermalization occurs for observables within a subsystem.
  • To investigate the behavior of entanglement entropies for subsystems of varying sizes.

Main Methods:

  • Formulating subsystem ETH using reduced density matrices of quantum subsystems.
  • Analyzing the limits of small and comparable subsystem sizes relative to their complements.
  • Calculating volume-proportional contributions to von Neumann and Rényi entanglement entropies.
  • Conducting numerical simulations on a one-dimensional Ising spin chain.

Main Results:

  • Subsystem ETH precisely defines the observables within a subsystem that exhibit eigenstate thermalization.
  • The study outlines methods for calculating entanglement entropies in specific subsystem size regimes.
  • Numerical evidence supporting the subsystem ETH formulation was obtained from the Ising spin chain model.

Conclusions:

  • Subsystem ETH offers a strong formulation of thermalization for subsystems in chaotic quantum systems.
  • The proposed framework provides insights into the relationship between quantum information and thermalization.
  • The findings are validated by numerical simulations, confirming the utility of subsystem ETH.