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arXiv:2604.02584 · The Journal of Chemical Physics

Fermionic mean-field dynamics for spin systems beyond free fermions

Rishab Dutta, Marc Illa, Niranjan Govind, Karol Kowalski

cond-mat.str-elquant-phSubmitted Apr 2, 2026• Announced Apr 6, 2026• 1 citation

v1 · Apr 2, 2026 v2 · May 22, 2026

Abstract

We introduce the fermionized time-dependent Hartree-Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact dynamics in the case of free fermions and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time steps. We benchmark fTDHF against exact dynamics on three separate spin-1/2 models, representing adiabatic preparation of states with long-range correlations, disorder-driven observation of many-body localization, and particle production in the Schwinger model. For each of these systems, fTDHF is shown to reproduce the qualitative dynamics generated by the exact evolutions, while maintaining a simple physical picture due to its mean-field nature.

Journal reference: J. Chem. Phys. 164, 234109 (2026)
DOI: 10.1063/5.0336867
Comments: 13 pages including references, 4 figures

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