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TT: Fachverband Tiefe Temperaturen
TT 22: Many-body Systems: Equilibration, Chaos, and Localization (joint session DY/TT)
TT 22.1: 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 sytems with long-range hoppings 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 modern developments on ergodicity breaking and localization in interacting quantum many-body systems, we 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. 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