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TT: Fachverband Tiefe Temperaturen
TT 25: Nonequilibrium Quantum Systems I (joint session TT/DY)
TT 25.11: Talk
Tuesday, March 19, 2024, 12:15–12:30, H 3005
Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems — •jiaozi wang1, jonas richter2,3, mats lamann1, robin steinigeweg1, jochen gemmer1, and anatoly dymarsky4 — 1U Osnabrück, Germany — 2U Stanford, USA — 3LU Hannover, Germany — 4U Kentucky, USA
We study statistical properties of matrix elements entering the eigenstate thermalization hypothesis by studying the observables written in the energy eigenbasis and truncated to small micro- canonical windows. We put forward a picture, that below certain energy scale collective statistical properties of matrix elements exhibit emergent unitary symmetry. In particular, below this scale the spectrum of the microcanonically truncated operator exhibits universal behavior for which we introduce readily testable criteria. We support this picture by numerical simulations and demonstrate existence of emergent unitary symmetry scale for all considered operators in chaotic many-body quantum systems. We discuss operator and system-size dependence of this energy scale and put our findings into context of previous works exploring emergence of random-matrix behavior in narrow energy windows.
[1] J. Wang, M. Lamann, J. Richter, R. Steinigeweg, A. Dymarsky, J. Gemmer, Phys. Rev. Lett. 128 (2022) 180601
[2] J. Wang, J. Richter, M. H. Lamann, R. Steinigeweg, J. Gemmer, A. Dymarsky, arXiv: 2310.20264 (2023)
Keywords: quantum chaos; spin systems; random matrix theory; eigenstate thermalization hypothesis