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Testing whether all eigenstates obey the eigenstate thermalization hypothesis.

Hyungwon Kim1, Tatsuhiko N Ikeda2, David A Huse1

  • 1Physics Department, Princeton University, Princeton, New Jersey 08544, USA.

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|December 11, 2014
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Summary
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The eigenstate thermalization hypothesis (ETH) holds strongly, even for extreme outliers in large quantum systems. Periodically driven systems show even better thermalization by removing energy conservation constraints.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • The eigenstate thermalization hypothesis (ETH) posits that individual eigenstates of complex quantum systems thermalize.
  • Investigating ETH in the strong sense requires examining every eigenstate in the thermodynamic limit.

Purpose of the Study:

  • To test the validity of the eigenstate thermalization hypothesis (ETH) in a strong sense.
  • To identify and analyze eigenstates that deviate from ETH predictions (outliers).

Main Methods:

  • Exact diagonalization of two 1D nonintegrable models: a quantum Ising chain and hard-core bosons.
  • Analysis of expectation values of few-body operators in highly excited many-body eigenstates.
  • Numerical simulations of periodically driven quantum systems (Floquet theory).

Main Results:

  • Extreme eigenstate outliers were found to obey ETH as system size increased.
  • Numerical evidence supports the strong form of ETH for the studied models.
  • Periodically driven Ising model eigenstates demonstrated even closer adherence to ETH.

Conclusions:

  • The findings provide strong numerical support for the eigenstate thermalization hypothesis in the thermodynamic limit.
  • Removing energy conservation via periodic driving enhances thermalization in quantum systems.