Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 39: Quantum Chaos (joint session DY/TT)

DY 39.7: Talk

Wednesday, March 18, 2020, 16:45–17:00, HÜL 186

New insights on the semiclassical study of many-body interference in Fermionic Fock space: a path integral approach — •Wolfgang Hogger, Juan-Diego Urbina, Falk Bruckmann, and Klaus Richter — Universität Regensburg

A long standing goal of quantum chaos is to establish the classical limit of Fermionic fields and to follow the corresponding semiclassical program. Following Gutzwiller, we propose to apply the stationary phase approximation to the coherent state path integral for bosons on a lattice and transforming a Fermionic system into the latter by subsequent use of Jordan-Wigner transformation and Schwinger-boson mapping. However, it was shown by Wilson and Galitzki in PRL 106, 110401 (2011) how the coherent state path integral breaks down for the Bose-Hubbard model and simple spin systems. Since the issues with the partition function path integral for the aforementioned systems were solved by Bruckmann and Urbina in arXiv:1807.10462v1 through dualization (a known method from lattice quantum field theories), the correct perturbative expansion is now correctly reproduced and one can obtain a path integral for the propagator as well. As a second key ingredient, thanks to a novel transformation in the spirit of Jordan-Wigner providing an exact map from many Fermionic degrees of freedom to a single large spin, we now obtain also a well-defined classical limit. Combining these two insights, a semi-classical theory of generic Fermi-Hubbard models is finally constructed and applied to some simple examples.