Local integrals of motion in the two-site Anderson-Hubbard model

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems

Background:

• Many-body localized (MBL) systems exhibit properties distinct from ergodic systems.
• Describing MBL states often involves conserved local pseudospins, but their optimal identification is challenging.
• Disorder plays a crucial role in the behavior of strongly correlated systems.

Purpose of the Study:

• To identify and characterize optimally local pseudospins in the disordered Hubbard model.
• To explore the distribution of possible pseudospin choices.
• To understand how these pseudospins evolve as system parameters change.

Main Methods:

• Numerical study of a small Anderson-Hubbard model.
• Analysis of local integrals of motion.
• Tracking pseudospin evolution with varying hopping and interaction parameters.

Main Results:

• Concrete examples of local integrals of motion in the Anderson-Hubbard model were provided.
• The most local pseudospin choice was identified.
• The distribution of possible pseudospin choices was explored.
• The evolution of optimally localized pseudospins was tracked away from the atomic limit.

Conclusions:

• The study provides a concrete method for identifying optimal pseudospins in MBL systems.
• Understanding pseudospin localization is key to comprehending disorder effects in correlated systems.
• The findings offer insights into the transition from localized to delocalized behavior.