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Subsystem eigenstate thermalization hypothesis for translation invariant systems.

Zhiqiang Huang1, Xiao-Kan Guo2

  • 1State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, <a href="https://ror.org/034t30j35">Chinese Academy of Sciences</a>, Wuhan 430071, China.

Physical Review. E
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This summary is machine-generated.

This study proves the subsystem eigenstate thermalization hypothesis for quantum systems without using random matrices. Researchers established bounds on quantum variance and relative entropy, demonstrating an algebraic convergence speed for thermalization in quantum lattice models.

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Area of Science:

  • Quantum physics
  • Statistical mechanics

Background:

  • The eigenstate thermalization hypothesis (ETH) explains thermalization in isolated quantum systems.
  • Previous proofs for translation-invariant systems relied on random matrix theory.

Purpose of the Study:

  • To prove the subsystem ETH for translation-invariant quantum systems without using random matrices.
  • To provide an elementary proof with an algebraic speed of convergence.

Main Methods:

  • Establishing a relationship between quantum variance and Belavkin-Staszewski relative entropy.
  • Deriving small upper bounds for these quantities.

Main Results:

  • The subsystem ETH is proven for translation-invariant quantum systems.
  • An algebraic speed of convergence for thermalization is demonstrated.
  • The proof applies to quantum lattice models with decaying correlations.

Conclusions:

  • A novel, elementary proof of the subsystem ETH is presented.
  • The findings extend the applicability of ETH to a broader class of quantum systems.
  • This work offers new insights into thermalization dynamics in quantum many-body systems.