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This study investigates many-body localization (MBL) in Heisenberg spin chains. Researchers found weak interactions cause instability, while strong disorder leads to MBL, with unique spin-correlation behaviors observed.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Physics

Background:

  • The nature of high-energy behavior in Heisenberg spin chains with random magnetic fields remains debated.
  • Understanding many-body localization (MBL) is crucial for quantum systems.

Purpose of the Study:

  • To explore the weak interaction limit of Anderson localized (AL) insulators.
  • To map the phase diagram of the XXZ model in the disorder-interaction plane.
  • To characterize the behavior of spin-spin correlation functions in different regimes.

Main Methods:

  • Shift-invert diagonalization was employed.
  • The study analyzed the XXZ model in the disorder (h) and interaction (Δ) plane.
  • Total magnetization conservation was utilized to analyze correlation functions.

Main Results:

  • Below a disorder threshold (h*), weak interactions induce ergodic instability.
  • At strong disorder, Anderson localized insulators transition directly to MBL.
  • Spin-spin correlation functions exhibit an orientation inversion (ξz > ξx) in the MBL regime.
  • Longitudinal correlation length (ξz) indicates ergodic instabilities, increasing with system size near the thermal phase.

Conclusions:

  • The study clarifies the transition from Anderson localization to many-body localization.
  • A novel indicator for ergodic instabilities, the longitudinal correlation length, was identified.
  • The findings contribute to a deeper understanding of quantum phase transitions in disordered spin systems.