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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • The eigenstate thermalization hypothesis (ETH) is a fundamental concept in quantum statistical mechanics.
  • ETH explains how isolated quantum systems can thermalize, reaching a state of maximum entropy.
  • Verifying ETH is crucial for understanding thermalization in quantum many-body systems.

Purpose of the Study:

  • To verify the universal applicability of the eigenstate thermalization hypothesis (ETH).
  • To investigate the role of local interactions in quantum system thermalization.
  • To explore deviations from conventional random matrix theory in the context of ETH.

Main Methods:

  • Introduction of random matrix ensembles with local interactions.
  • Numerical computation of the distribution of maximum fluctuations of eigenstate expectation values.
  • Comparison of results with conventional random matrix theory.

Main Results:

  • Demonstrated that an overwhelming majority of local Hamiltonians and observables satisfy ETH.
  • Observed exponentially small fluctuations in eigenstate expectation values.
  • Identified a breakdown of ergodicity in random matrix ensembles due to locality, a phenomenon not captured by conventional random matrix theory.

Conclusions:

  • The eigenstate thermalization hypothesis (ETH) holds universally for locally interacting quantum many-body systems.
  • Local interactions lead to exponentially small fluctuations, supporting ETH.
  • Novel random matrix ensembles are necessary to capture the physics of local interactions and ETH.