Efficient classical simulation of time dynamics in Fermi-Hubbard models with imaginary interactions

TL;DR

This paper introduces an efficient classical algorithm for simulating the time dynamics of Fermi-Hubbard models with imaginary interactions by mapping them to Lindbladian evolution of free fermions, enabling better understanding of complex quantum systems.

Contribution

It presents a novel classical simulation method for imaginary-interaction Fermi-Hubbard models using a Lindbladian evolution mapping, building on recent algorithms for mixed unitary channels.

Findings

Efficient classical algorithm for specific Fermi-Hubbard models

Mapping between Lindbladian evolution and imaginary-interaction models

Discussion on classical complexity for general parameters

Abstract

Using a map between the Lindbladian evolution of dephasing in free fermions and the time evolution of imaginary-interaction Fermi-Hubbard models in bipartite lattices, we present an efficient classical algorithm to solve the Schr\"{o}dinger equation in these interacting systems. This algorithm leverages the recently discovered algorithm for simulating Lindbladian evolution by sampling mixed unitary channels (Wang et al arXiv:2601.06298). We comment on the expected classical complexity of the problem for general complex values of the parameters and discuss some applications.