Interaction-Driven Instabilities in the Random-Field XXZ Chain

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.