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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Physics

Background:

  • Many-body localization (MBL) is a phenomenon where quantum systems fail to thermalize due to strong interactions.
  • Characterizing the MBL transition in closed fermionic systems remains a challenge.

Purpose of the Study:

  • To demonstrate the utility of the one-particle density matrix (ρ) in characterizing the interaction-driven MBL transition.
  • To explore how properties derived from ρ, such as natural orbitals and occupation spectra, behave across the MBL transition.

Main Methods:

  • Analysis of the one-particle density matrix (ρ) and its properties.
  • Calculation and analysis of natural orbitals (eigenstates of ρ) and their localization.
  • Examination of the occupation spectrum (eigenvalues of ρ) and its structure.
  • Computation of one-particle occupation entropy and inverse participation ratio (IPR) of natural orbitals.

Main Results:

  • Natural orbitals localize in the MBL phase and delocalize in the ergodic phase.
  • The occupation spectrum exhibits a steplike discontinuity in the MBL phase, revealing Fock-space structure.
  • One-particle occupation entropy is low in the MBL phase and high in the ergodic phase, with diverging fluctuations at the transition.
  • The IPR of natural orbitals is system-size independent in the MBL phase.

Conclusions:

  • The one-particle density matrix provides a robust framework for understanding and characterizing the MBL transition in closed fermionic systems.
  • Properties derived from ρ, including natural orbitals and occupation spectra, serve as effective order parameters for distinguishing MBL and ergodic phases.
  • The findings offer a new perspective on the nature of quantum localization and thermalization in interacting quantum systems.