Three-body correlations in the Nagaoka state on the square lattice

TL;DR

This paper develops a three-body scattering theory to analyze the Nagaoka ferromagnetic state in the 2D Hubbard model, highlighting the significance of three-body correlations and proposing an improved phase boundary for the ground state.

Contribution

The paper introduces a new three-body scattering approach applied to the Nagaoka state, enhancing understanding of correlations beyond ladder approximation and refining phase boundary predictions.

Findings

Three-body correlations significantly affect the Nagaoka state.

The developed theory improves phase boundary estimates.

Comparison with ladder approximation shows the importance of three-body effects.

Abstract

A three-body scattering theory previously proposed by one of the present authors is developed to be applied to the saturated ferromagnetic state in the two-dimensional Hubbard model. The single-particle Green's function is calculated by taking account of the multiple scattering between two electrons and one hole. Several limiting cases are discussed and the relation to the variational principle is examined. The importance of the three-body correlation is demonstrated in comparison with the results of the ladder approximation. A possible phase boundary for the Nagaoka ground state is presented for the square lattice, which improves the previous variational results.