Fermionic mean-field dynamics for spin systems beyond free fermions

TL;DR

The paper presents fTDHF, a fermionized time-dependent Hartree-Fock method for simulating spin-1/2 systems, capable of handling long-range interactions efficiently and reproducing key dynamics qualitatively.

Contribution

Introduction of fTDHF, a scalable mean-field approach for spin systems mapped to fermions, extending beyond free fermion models.

Findings

fTDHF reproduces qualitative dynamics of complex spin models

Method scales polynomially with system size and linearly with time steps

Benchmarks show good agreement with exact dynamics in various models

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.