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DY: Fachverband Dynamik und Statistische Physik
DY 17: Many-body Systems: Equilibration, Chaos, and Localization (joint session DY/TT)
DY 17.13: Talk
Tuesday, March 19, 2024, 12:45–13:00, A 151
Critical quantum dynamics of observables at eigenstate transitions — Simon Jiricek1, •Miroslav Hopjan2, Patrycja Łydzba3, Fabian Heidrich-Meisner1, and Lev Vidmar2,4 — 1Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany — 2Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia — 3Department of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland — 4Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
It is an outstanding goal to unveil the fingerprints of universal quantum dynamics at eigenstate transitions. Focusing on quadratic fermionic Hamiltonians, we identify physical observables that exhibit critical behavior at the transition. Our result is based on two ingredients: (a) A relationship between the observable time evolution in a many-body state and the transition probabilities in single-particle states, and (b) a scale invariance of transition probabilities, which generalizes the recent result for survival probabilities [1]. We then show that these properties give rise to a critical behavior in the quantum quench dynamics of observables, which share the common eigenbasis with the Hamiltonian before the quench. We numerically demonstrate this phenomenon at the localization transition in the three-dimensional Anderson model, for which the critical bahavior can be detected in experimentally relevant observables such as site occupations and particle imbalance. [1] M. Hopjan and L.Vidmar, Phys. Rev. Lett. 131, 060404 (2023)
Keywords: Anderson localization; Eigenstate transitions; Quantum chaos; Quantum quench; Disordered systems