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Eigenstate Thermalization for Degenerate Observables.

Fabio Anza1,2, Christian Gogolin3, Marcus Huber4

  • 1Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.

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|May 15, 2018
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Summary
This summary is machine-generated.

The eigenstate thermalization hypothesis (ETH) explains how quantum systems reach equilibrium. This study shows that for highly degenerate observables, ETH is verified when relative phases do not cumulatively conspire, paving the way for thermalization proofs.

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Area of Science:

  • Quantum statistical mechanics
  • Condensed matter theory
  • Quantum information

Background:

  • Expectation values of observables often approach equilibrium statistical mechanics predictions under unitary time evolution.
  • The eigenstate thermalization hypothesis (ETH) posits this occurs even for individual energy eigenstates.

Purpose of the Study:

  • To elucidate the emergence of ETH for realistically measurable observables (local, extensive, macroscopic) with high degeneracy.
  • To identify conditions under which these observables satisfy the ETH.

Main Methods:

  • The problem is divided into two conditions: relative overlaps and relative phases between observable and Hamiltonian eigenbases.
  • Analysis of unbiased relative overlaps for highly degenerate observables.

Main Results:

  • Relative overlaps are shown to be unbiased for highly degenerate observables.
  • Observables verify ETH unless relative phases exhibit cumulative effects.

Conclusions:

  • The study elucidates pathways towards proving thermalization for degenerate observables.
  • Demonstrates the critical role of relative phases in verifying ETH.