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Eigenstate Thermalization in Long-Range Interacting Systems.

Shoki Sugimoto1, Ryusuke Hamazaki2, Masahito Ueda1,3

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Summary
This summary is machine-generated.

The strong eigenstate thermalization hypothesis generally holds for long-range quantum systems (α≥0.6). However, deviations from the microcanonical ensemble average are significant, and Srednicki's ansatz fails for weaker long-range interactions (α≲1.0).

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Area of Science:

  • Quantum physics
  • Statistical mechanics

Background:

  • Recent ion experiments explore tunable long-range interacting quantum systems.
  • The eigenstate thermalization hypothesis (ETH) describes thermalization in isolated quantum systems.

Purpose of the Study:

  • To test the strong ETH for quantum systems with power-law interactions (∼1/r^{α}).
  • To investigate deviations from the microcanonical ensemble average in long-range interacting systems.
  • To assess the validity of Srednicki's ansatz for these systems.

Main Methods:

  • Numerical simulations of quantum systems with power-law interactions.
  • Analysis of local observables and their expectation values.
  • Comparison with microcanonical ensemble averages.

Main Results:

  • The strong ETH typically holds for α≥0.6, encompassing Coulomb, monopole-dipole, and dipole-dipole interactions.
  • Significant deviations between eigenstate expectation values and microcanonical averages observed in long-range systems.
  • Srednicki's ansatz breaks down for α≲1.0, particularly in larger systems.

Conclusions:

  • The ETH is robust for a range of long-range interactions, but thermalization properties differ from short-range systems.
  • The breakdown of Srednicki's ansatz highlights limitations in describing thermalization in certain long-range quantum systems.