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TT: Fachverband Tiefe Temperaturen

TT 38: Nonequilibrium Quantum Many-Body Systems II (joint session TT/DY)

TT 38.3: Talk

Wednesday, March 29, 2023, 15:30–15:45, HSZ 204

Rate functions and the approach to adiabaticity in quantum many body systems — •Vibhu Mishra, Salvatore Manmana, and Stefan Kehrein — Institute for Theoretical Physics, Georg-August-Universität Goettingen, Friedrich-Hund-Platz 1, 37077 Goettingen

The quantum adiabatic theorem is a fundamental result in quantum mechanics with applications ranging from quantum adiabatic computation to topological systems, while also serving as a theoretical foundation to many body perturbation theory via the Gell-Mann Low theorem.

We establish an inherent competition between ramp times T for an adiabatic process vs the system size N, in the behavior of relevant many body overlaps. We study this interplay between T and N by analyzing the properties of rate functions which are defined to be intensive quantities that give us a quantitative measure of the deviation from adiabaticity in the thermodynamic limit.

We analyze the Transverse Field Ising Model and the XXZ chain in 1D using exact diagonalization. We find that the rate functions show algebraic decay with increasing ramp time T. The decay exponent of the rate function for ramps within the gapped phase is 2, for ramps across Ising critical point it is 0.5 and within the Luttinger Liquid phase it is 1. The immediate implication is that the many body adiabatic time scales grow unavoidably with system size, namely as the √N for ramps within the gapped phase, and with N within the Luttinger Liquid phase.