SKM 2023 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 25: Many-Body Quantum Dynamics (joint session DY/TT)
DY 25.1: Hauptvortrag
Mittwoch, 29. März 2023, 09:30–10:00, MOL 213
Many-body localization from Hilbert- and real-space points of view — •Ivan Khaymovich1, Giuseppe De Tomasi2, Frank Pollmann3, and Simone Warzel3 — 1Nordic Institute for Theoretical Physics, Stockholm, Sweden — 2University of Illinois Urbana-Champaign, USA — 3Technical University Munich, Germany
Many-body localization (MBL), known as a generic mechanism to break quantum ergodicity, has been recently shown to be not the Hilbert-space Anderson localization. Instead, the MBL eigenstate occupies a fractal support [1-2], with extensive number of configurations. On the other hand, the well-established and accepted by the community picture of an emergent set of local integrals of motion [3] provides the structure of the MBL in the real space.
In this talk, I will provide the observable (later measured in the experiment [4]) which combines the fractality in the Hilbert space with the presence of local integrals of motion [2]. This observable, being the radial profile of the eigenstate over the Hamming distance, keeps the information about both the Hilbert-space fractal dimensions and the real-space localization lengths and uncovers the structure of these measures across the MBL transition. Phenomenological picture behind this behavior is consistent with the Kosterlitz-Thouless scenario of the MBL transition, suggested in the literature.
Literature: [1] N. Macé et al., PRL 123, 180601 (2019). [2] G. De Tomasi, I. M. Khaymovich et al. PRB 104, 024202 (2021). [3] Abanin et al., RMP 91, 021001 (2019). [4] Y. Yao et al arXiv:2211.05803.