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Eigenstate Thermalization from the Clustering Property of Correlation.

Tomotaka Kuwahara1,2, Keiji Saito3

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The clustering property in quantum systems links to thermalization. Eigenstate thermalization occurs in low-energy, sparse states, while high-energy states show ensemble equivalence and weak thermalization.

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Area of Science:

  • Quantum Many-Body Physics
  • Statistical Mechanics
  • Thermodynamics

Background:

  • The clustering property of equilibrium bipartite correlations is a general thermodynamic property in noncritical quantum systems.
  • Understanding thermalization in these systems is crucial for comprehending their thermodynamic behavior.

Purpose of the Study:

  • To investigate the thermalization properties of quantum systems exhibiting the clustering property.
  • To explore the connection between the clustering property, density of states, and eigenstate thermalization.

Main Methods:

  • Analysis of systems with the clustering property across high- and low-energy regimes.
  • Investigation of the density of states and its relation to thermalization properties.
  • Demonstration of ensemble equivalence in specific energy regimes.

Main Results:

  • The clustering property is linked to eigenstate thermalization via the density of states.
  • Eigenstate thermalization is observed in the low-energy regime with a sparse density of states (typical of gapped systems).
  • Ensemble equivalence (microcanonical and canonical) is shown for high-energy regimes, even with small energy shells, leading to weak eigenstate thermalization.

Conclusions:

  • The clustering property provides a unified framework for understanding thermalization in certain quantum systems.
  • The density of states plays a critical role in determining the thermalization behavior across different energy regimes.
  • This work elucidates the conditions under which different forms of eigenstate thermalization emerge in many-body quantum systems.