Two Theorems on Pseudo-spin in the Hubbard Model

TL;DR

This paper derives an eigenvalue inequality for the reduced density matrix in the Hubbard model and examines symmetry-breaking effects on pseudo-spin quasi-averages, contributing to the theoretical understanding of quantum correlations.

Contribution

It introduces new inequalities for eigenvalues of the reduced density matrix and analyzes pseudo-spin symmetry-breaking in the Hubbard model.

Findings

Eigenvalue inequality for $ ho_2$ at finite temperature

Zero quasi-average of $ ilde{S}^{+}$ under symmetry-breaking perturbation

Insights into pseudo-spin behavior in the Hubbard model

Abstract

An inequality of the eigenvalues of the reduced density matrix $\rho_2$ at finite temperature in the Hubbard model is obtained by means of the Bogolyubov inequality. The quasi-average of $\tilde{S}^{+}$ in a simple symmetry-breaking perturbation of the Hamiltonian for a bipartite lattice is shown to be zero.