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The study investigates the conditions for a many-body localization (MBL) phase, where thermalization fails even at infinite system sizes. Numerical findings show persistent drifts towards ergodicity, complicating the understanding of the MBL phase boundary.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • The eigenstate thermalization hypothesis (ETH) explains thermalization in isolated quantum systems via ergodicity and chaos.
  • Many-body localization (MBL) is a regime where thermalization fails in disordered systems, but the conditions for a true MBL phase remain unclear.

Purpose of the Study:

  • To review recent numerical investigations on the MBL phase.
  • To clarify the critical open questions regarding the dynamics of disordered many-body systems.
  • To provide a unified understanding of various tools and indicators used to study the breakdown of ergodicity.

Main Methods:

  • Analysis of spectral and wave function measures.
  • Examination of matrix elements of observables.
  • Probing unitary quantum dynamics, transport, and quantum information measures.
  • Review of numerical methods for studying ETH and MBL.

Main Results:

  • Persistent finite-size drifts towards ergodicity are observed in disordered systems, even at strong disorder.
  • These drifts indicate continuous movement towards ergodicity and non-vanishing transport.
  • Trends exclude naive single-parameter scaling, necessitating refined scaling procedures.

Conclusions:

  • The MBL phase boundary remains elusive due to persistent drifts towards ergodicity.
  • Understanding microscopic processes at the ETH-MBL crossover is challenging.
  • Further exploration is needed to fully understand thermalization and its failure in disordered many-body systems.