Symmetry Properties on Magnetization in the Hubbard Model at Finite Temperatures

TL;DR

This paper derives fundamental symmetry-based relations between magnetization and spin correlations in the Hubbard model at finite temperatures, applicable across dimensions, interaction types, and electron fillings.

Contribution

It introduces symmetry-derived relations akin to Ward-Takahashi identities for magnetization in the Hubbard model, broadening understanding of magnetic properties.

Findings

Relations hold for all dimensions (1D, 2D, 3D)

Applicable to both repulsive and attractive interactions

Valid for arbitrary electron fillings

Abstract

By making use of some symmetry properties of the relevant Hamiltonian, two fundamental relations between the ferromagnetic magnetization and a spin correlation function are derived for the $d (=1,2,3)$-dimensional Hubbard model at finite temperatures. These can be viewed as a kind of Ward-Takahashi identities. The properties of the magnetization as a function of the applied field are discussed. The results thus obtained hold true for both repulsive and attractive on-site Coulomb interactions, and for arbitrary electron fillings.