Accessing Many-Body Localized States through the Generalized Gibbs Ensemble

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics

Background:

• Many-body localization (MBL) is a phenomenon where quantum systems fail to thermalize due to disorder.
• Studying the thermodynamic properties of MBL systems is crucial for understanding their unique behavior.
• Previous methods faced challenges in simulating large MBL systems and higher dimensions.

Purpose of the Study:

• To develop a novel computational method for studying the thermodynamic properties of large many-body localized systems.
• To overcome limitations of existing simulation techniques for MBL systems.
• To explore the possibility of a fully many-body localized phase in two-dimensional systems.

Main Methods:

• Utilized quantum Monte Carlo simulations.
• Devised a heuristic approach to construct high-quality local integrals of motion.
• Incorporated these integrals into the Hamiltonian using Lagrange multipliers.
• Simulated the ground state of the shifted Hamiltonian.

Main Results:

• The proposed method effectively studies thermodynamic properties of many-body localized systems.
• The simulations reveal that weak mixing between eigenstates preserves MBL characteristics, unlike standard statistical mechanics ensembles.
• The approach is suitable for studying higher dimensions.

Conclusions:

• The developed quantum Monte Carlo method provides a viable pathway to investigate large many-body localized systems.
• The findings suggest the likely existence of a fully many-body localized phase in two dimensions.
• This work opens new avenues for exploring MBL in various dimensions and system sizes.