Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• The power-law banded random matrix (PLBRM) ensemble is studied.
• Its interpretation as Hamiltonians for one-dimensional quantum many-body systems is explored.
• Labeling schemes for assigning random matrix basis indices to many-body basis vectors are introduced and compared.

Purpose of the Study:

• To compare the physical properties of Hamiltonians derived from different PLBRM interpretations.
• To focus on the half-system eigenstate bipartite entanglement entropy as a key property.
• To demonstrate and quantify how known PLBRM phases relate to entanglement transitions in quantum many-body systems.

Main Methods:

• Introduction and comparison of various labeling schemes.
• Analysis of Hamiltonians derived from PLBRM ensembles.
• Calculation and analysis of half-system eigenstate bipartite entanglement entropy.
• Scaling analysis of spectral edge and bulk eigenstates in the weakly ergodic phase.

Main Results:

• Different PLBRM phases (ergodic, weakly ergodic, localized) are shown to correspond to entanglement transitions.
• A quantitative picture of boundaries between entanglement scaling behaviors is provided for the weakly ergodic phase.
• An intermediate set of eigenstates with volume law entanglement scaling and nonvanishing deviation from the Page value is identified.

Conclusions:

• The quantum many-body interpretation of PLBRM ensembles reveals entanglement transitions.
• The study quantifies these transitions and characterizes intermediate eigenstate behaviors.
• Findings provide insights into the relationship between random matrix theory and quantum entanglement.