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Many-body localization in periodically driven systems.

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Researchers identified two distinct phases in disordered quantum systems: a many-body localized (MBL) phase with area-law entanglement and a delocalized phase with volume-law entanglement. The MBL phase shows logarithmic entanglement growth, distinguishing it from the delocalized phase.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Disordered quantum systems with time-dependent Hamiltonians are crucial for understanding complex phenomena.
  • Floquet eigenstates and entanglement entropy are key indicators of system phases.
  • The eigenstate thermalization hypothesis (ETH) describes thermalization in quantum systems.

Purpose of the Study:

  • To identify and characterize distinct phases in one-dimensional disordered many-body systems with periodic time-dependent Hamiltonians.
  • To investigate the properties of Floquet eigenstates, including entanglement entropy and adherence to the ETH.
  • To propose an effective model for the many-body localized (MBL) phase.

Main Methods:

  • Analysis of Floquet eigenstates in disordered quantum systems.
  • Calculation of entanglement entropy (area-law vs. volume-law).
  • Numerical simulations using exact diagonalization and time-evolving block decimation (TEBD).

Main Results:

  • Identification of two distinct phases: a many-body localized (MBL) phase and a delocalized phase.
  • The MBL phase exhibits area-law entanglement and violates the ETH, while the delocalized phase shows volume-law entanglement and obeys the ETH.
  • The MBL phase demonstrates logarithmic in time growth of entanglement entropy from a product state, unlike the delocalized phase.

Conclusions:

  • A direct phase transition exists between the MBL and delocalized phases.
  • An effective model based on emergent local integrals of motion explains the MBL phase's properties.
  • The study provides a framework for understanding localization and thermalization in driven quantum systems.