Fermi Machine -- Quantum Many-Body Solver Derived from Correspondence between Noninteracting and Strongly Correlated Fermions

TL;DR

This paper introduces a novel quantum many-body solver called Fermi Machine, which leverages a correspondence between interacting and non-interacting fermions, enabling neural network-based solutions for Hubbard models.

Contribution

It formulates a formalism linking strongly correlated and non-interacting fermions, and develops a neural network approach for solving Hubbard models based on this correspondence.

Findings

Exact correspondence demonstrated for 1- and 2-site Hubbard models

Numerical algorithm successfully applied to 4-site systems

Promising future directions discussed

Abstract

Stimulated by the successful descriptions of strongly correlated electron systems by fractionalized fermions, correspondence between interacting fermions and non-interacting multi-component fermions is formulated in examples of the Hubbard model. The formalism enables constructions of the neural network for a quantum many-body solver represented by coupled noninteracting fermions. After showing the exact correspondence of 1- and 2-site Hubbard model to two-component noninteracting fermions, numerical algorithm of the quantum machine learning for the Hubbard model is proposed. Benchmark for the 4-site systems is successfully presented and promising future directions as well as implications are discussed.