SAMOP 2021 – scientific programme
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QI: Fachverband Quanteninformation
QI 12: Quantum Simulation and Many-Body Systems
QI 12.6: Talk
Friday, September 24, 2021, 12:30–12:45, H3
From non-Hermitian linear response to dynamical correlations and fluctuation–dissipation relations in quantum many-body systems — •Kevin T. Geier1,2 and Philipp Hauke1 — 1INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy — 2Institute for Theoretical Physics, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
Dynamical correlations encode a plethora of fundamental properties in quantum many-body systems. An outstanding role is played by the fluctuation–dissipation relation (FDR), which connects the intrinsic fluctuations of a system in thermal equilibrium across the entire frequency spectrum with the energy dissipated in response to a perturbation. Out of equilibrium, independent measurements of both sides of the FDR could serve as an unbiased probe of thermalization in closed quantum systems. Yet, while the dissipation side is commonly probed in linear response experiments, it is by far more challenging to access the fluctuation side experimentally. Here, we show that the linear response to a non-Hermitian perturbation can be used to measure unequal-time anti-commutators, giving direct access to the fluctuation side of the FDR [1]. We present specific protocols to realize the required non-Hermitian dynamics in cold-atom systems, which we illustrate through numerical simulations of a Bose–Hubbard system.
Our framework provides a general and flexible way to characterize dynamical correlations in strongly correlated matter on a variety of platforms.
[1] K. T. Geier and P. Hauke, arXiv:2104.03983 [cond-mat.quant-gas].