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Anomalous Thermalization in Ergodic Systems.

David J Luitz1, Yevgeny Bar Lev2

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Quantum systems satisfying the eigenstate thermalization hypothesis (ETH) can exhibit anomalous subdiffusive thermalization, challenging the assumption of diffusive behavior. This study reveals a modified ETH and links operator variance scaling to anomalous transport dynamics.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • The eigenstate thermalization hypothesis (ETH) is a cornerstone for understanding thermalization in isolated quantum systems.
  • ETH typically implies diffusive thermalization dynamics, where local observables equilibrate over time.

Purpose of the Study:

  • To challenge the restrictive assumption that all ETH-satisfying systems are diffusive.
  • To investigate systems exhibiting anomalous, subdiffusive thermalization.
  • To establish a general connection between operator matrix element scaling and anomalous transport.

Main Methods:

  • Developing a modified ETH ansatz for subdiffusive systems.
  • Deriving a general relationship between the variance of off-diagonal matrix elements and the dynamical exponent.
  • Numerical simulations on the random field Heisenberg chain to study eigenfunction distributions and operator matrix elements.

Main Results:

  • Identified quantum systems that are asymptotically thermal but display subdiffusive thermalization.
  • Demonstrated that the variance of off-diagonal matrix elements scales slower with system size in subdiffusive systems compared to diffusive ones.
  • Observed non-Gaussian distributions of eigenfunctions in the random field Heisenberg chain, violating Berry's conjecture.

Conclusions:

  • The assumption of diffusive thermalization in ETH systems is too restrictive.
  • Subdiffusive thermalization is possible and linked to specific scaling properties of operator matrix elements.
  • The random field Heisenberg chain exhibits anomalous transport and violates Berry's conjecture, highlighting complex quantum dynamics.