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DY: Fachverband Dynamik und Statistische Physik

DY 17: Many-body Systems: Equilibration, Chaos, and Localization (joint session DY/TT)

DY 17.3: Talk

Tuesday, March 19, 2024, 10:00–10:15, A 151

Long-range spectral statistics of the Rosenzweig-Porter model — •Wouter Buijsman — Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

The Rosenzweig-Porter model is a single-parameter random matrix ensemble that supports an ergodic, fractal, and localized phase. Introduced over sixty years ago, this model recently gained renewed interest as a toy model for the many-body localization transition. We construct a unitary (Floquet) equivalent of this model, for which we numerically study the long-range spectral statistics [1,2]. The construction is based on interpreting the Rosenzweig-Porter model as a Brownian quantum system [3]. Our main result is the observation that the transition between the ergodic and fractal phases can be probed through the spectral form factor. Complementing previous results on the level spacing distribution, this establishes that spectral statistics are sufficient to fully map out the phase diagram of the model. We quantitatively discuss the scaling of the Thouless time, and point out the possible universality of the spectral form factor at the transition between the fractal and the localized phases.

[1] W. Buijsman and Y. Bar Lev, Circular Rosenzweig-Porter random matrix ensemble, SciPost Phys. 12, 082 (2022).

[2] W. Buijsman, Long-range spectral statistics of the Rosenzweig-Porter model, arXiv:2309.14043 (2023).

[3] W. Buijsman, Efficient circular Dyson Brownian motion algorithm, arXiv: 2309.07457 (2023).

Keywords: Rosenzweig-Porter model; many-body localization; random matrix theory; spectral statistics; fractality