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Non-Abelian Eigenstate Thermalization Hypothesis.

Chaitanya Murthy1, Arman Babakhani2,3, Fernando Iniguez4

  • 1Department of Physics, Stanford University, Stanford, California 94305, USA.

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|April 21, 2023
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Summary
This summary is machine-generated.

The eigenstate thermalization hypothesis (ETH) is extended to quantum systems with noncommuting charges. This new framework, the non-Abelian ETH, explains thermalization in complex quantum systems, though sometimes slowly.

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Area of Science:

  • Quantum Many-Body Physics
  • Quantum Thermodynamics

Background:

  • The Eigenstate Thermalization Hypothesis (ETH) explains thermalization in quantum systems lacking symmetries.
  • Standard ETH assumes commuting conserved quantities, limiting its application to systems with noncommuting charges.

Purpose of the Study:

  • To extend the ETH to quantum systems with noncommuting charges.
  • To investigate thermalization dynamics in the presence of non-Abelian symmetries.

Main Methods:

  • Positing a non-Abelian ETH framework.
  • Utilizing approximate microcanonical subspaces from quantum thermodynamics.
  • Applying the non-Abelian ETH to systems with SU(2) symmetry.

Main Results:

  • Demonstrated that time averages of local operators generally thermalize under the non-Abelian ETH.
  • Identified specific cases where thermalization converges unusually slowly with system size.
  • Proved thermalization for many scenarios within the new framework.

Conclusions:

  • The non-Abelian ETH provides a robust extension of ETH for systems with noncommuting charges.
  • This work addresses recent challenges in quantum thermodynamics concerning noncommuting symmetries.
  • The findings offer insights into thermalization processes in complex quantum many-body systems.