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Entanglement-Ergodic Quantum Systems Equilibrate Exponentially Well.

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This study provides new insights into how many-body systems reach equilibrium under unitary time evolution. It shows that equilibration can be derived from a weak condition related to entanglement properties in energy eigenstates.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • Understanding equilibration in isolated quantum systems is a fundamental challenge in nonequilibrium physics.
  • Existing theories often rely on typicality arguments, lacking direct evidence for natural initial states.
  • Many-body localization and scars are related phenomena impacting system dynamics.

Purpose of the Study:

  • To establish rigorous conditions for equilibration in many-body systems without relying on typicality.
  • To investigate the role of Rényi entanglement entropies in energy eigenstates for equilibration.
  • To connect equilibration phenomena to the eigenstate thermalization hypothesis.

Main Methods:

  • Analysis of Rényi entanglement entropies in energy eigenstates.
  • Derivation of equilibration conditions from a weak assumption on entanglement properties.
  • Connecting findings to the eigenstate thermalization hypothesis framework.

Main Results:

  • Demonstrated stringent results for equilibration in systems where entanglement entropies are extensive.
  • Showed that equilibration can be derived from a condition weaker than typically assumed.
  • Reversed the usual logic by deriving equilibration from an eigenstate property.

Conclusions:

  • Equilibration in many-body systems can be rigorously established from specific entanglement properties of energy eigenstates.
  • The findings offer a new perspective on the conditions for thermalization in quantum systems.
  • This work provides a foundation for further studies on quantum dynamics and thermalization.