Regensburg 2025 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 16: Many-body Systems: Equilibration, Chaos, and Localization (joint session DY/TT)
DY 16.1: Vortrag
Dienstag, 18. März 2025, 14:00–14:15, H37
Power-law banded random matrices as models for quantum many-body Hamiltonians — •Wouter Buijsman1, Masudul Haque2,1, and Ivan M. Khaymovich3 — 1Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — 2TU Dresden, Institute of Theoretical Physics, Dresden, Germany — 3Nordita, Stockholm, Sweden
Hamiltonians of one-dimensional, disordered single-particle systems with long-range hopping terms can naturally be modeled by power-law banded random matrices. In this picture, the phase diagram of power-law banded random matrices show an ergodic, weakly ergodic, and localized phase. Motivated by recent developments on ergodicity breaking and localization in interacting quantum many-body systems, we numerically study many-body interpretations of such random matrices. We discuss a number of ways to label the basis states with many-body configurations, and compare the physical properties of the resulting Hamiltonians. Specifically, we study the scaling of the many-body entanglement entropy with system size for eigenstates at both the bulk and the edge of the spectra. Using a scaling analysis on the full sets of eigenstates, we subsequently provide a quantitative picture of the phase diagram, showing how the different types of scaling behaviour at the bulk and the edge are connected to each other. We elaborate on the physical relevance of this interpretation of random matrix models for quantum many-body systems.
Keywords: quantum many-body systems; long-range interactions; random matrix theory; ergodicity breaking; localization