Simple probability distributions on a Fock-space lattice

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• Many-body localization (MBL) is crucial for understanding quantum systems' thermalization properties.
• Disordered interacting fermion systems are standard models for MBL studies.
• Understanding the transition from localized to delocalized states is key.

Purpose of the Study:

• To analyze a standard model for many-body localization: interacting spinless fermions with quenched disorder.
• To investigate the model's behavior on d-dimensional hypercubic lattices at non-zero filling fractions.
• To explore the mapping to a Fock-space (FS) lattice and its implications.

Main Methods:

• Recasting the fermion model into an equivalent tight-binding model on a Fock-space (FS) lattice.
• Obtaining exact results in the thermodynamic limit for distributions of local FS coordination numbers, FS site-energies, and density of many-body states.
• Utilizing exact diagonalization for numerical analysis on modest system sizes.

Main Results:

• Distributions of local FS coordination numbers, FS site-energies, and density of many-body states were accurately determined.
• These distributions are well-captured by exact diagonalization on numerically tractable system sizes.
• The importance of choosing the correct variance for eigenvalue distributions for mobility edge identification was highlighted.

Conclusions:

• The Fock-space lattice approach provides an effective framework for studying disordered interacting fermion systems.
• Exact results and numerical methods confirm the model's behavior and distributions.
• Careful analysis of eigenvalue distributions is essential for robust identification of mobility edges in MBL studies.