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Eigenstate thermalization in systems with spontaneously broken symmetry.

Keith R Fratus1, Mark Srednicki1

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Strongly nonintegrable systems usually follow the eigenstate thermalization hypothesis. However, for observables with multiple thermal values due to broken symmetries, systems become unstable, forming new eigenstates that yield these values, as shown in the quantum Ising model.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • The eigenstate thermalization hypothesis (ETH) posits that energy eigenstates of nonintegrable systems capture thermal properties.
  • Observables that are order parameters for spontaneously broken symmetries present a challenge to ETH due to multiple possible thermal values.

Purpose of the Study:

  • To revise the eigenstate thermalization hypothesis for systems with spontaneously broken symmetries.
  • To investigate the behavior of such systems and provide evidence for a proposed mechanism.

Main Methods:

  • Numerical study of the two-dimensional transverse-field quantum Ising model.
  • Analysis of energy eigenstates and their expectation values for relevant observables.

Main Results:

  • Demonstrated that systems with order parameters for broken symmetries deviate from standard ETH predictions.
  • Provided strong numerical evidence for system instability towards forming new eigenstates.
  • Showcased that these new eigenstates correspond to the different possible thermal values.

Conclusions:

  • The eigenstate thermalization hypothesis requires revision in the presence of spontaneously broken symmetries.
  • Systems become unstable and form distinct eigenstates to realize each possible thermal value for order parameters.