Dresden 2026 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 63: Quantum Dynamics and Many-body Systems – Poster (joint session DY/TT)
TT 63.4: Poster
Wednesday, March 11, 2026, 15:00–18:00, P5
Quantum Chaos in a Classical Counterpart to the Fermi-Hubbard model through an exact Path-Integral Formalism — •Louis Renck1, Wolfgang Hogger2, Juan Diego Urbina2, and Peter Schlagheck1 — 1IPNAS, CESAM research unit, Université de Liège, Belgium — 2Institut für Theoretische Physik, Universität Regensburg, Germany
Understanding quantum chaos in interacting many-fermion systems remains challenging : unlike many-bosons systems - where quantum-classical correspondence can be established using semiclassical tools such as the van Vleck-Gutzwiller propagator [1] -, most interacting fermions models still lack a sensible classical limit where Hamiltonian chaos can be defined.
We propose a candidate to the first classical Hamiltonian for the Fermi-Hubbard model with integrability broken by a random onsite potential. Starting from the fermionic Hamiltonian, we apply a Jordan-Wigner transformation and switch to the Schwinger-boson representation to obtain a bosonic form. A recently developed exact bosonic path-integral formalism [2] then provides a classical Hamiltonian symbol defined over a symplectic phase space. We investigate the resulting quantum-classical correspondence by comparing the effective dynamics with the quantum evolution, and we present quantitative checks of chaos based on spectral properties and out-of-time ordered correlators.
[1]. T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014).
[2]. F. Bruckmann and J. D. Urbina (2018)
Keywords: Quantum Chaos; Hubbard Model; Semiclassical; Path Integral; Fermions