Exact Results of Strongly Correlated Systems at Finite Temperature

TL;DR

This paper derives rigorous finite-temperature results for strongly correlated models like the Hubbard, Kondo lattice, and Anderson models, revealing that certain spin expectation values scale with system size.

Contribution

It provides exact finite-temperature results for key strongly correlated models using fluctuation-dissipation and particle-hole transformations, a novel analytical achievement.

Findings

Expectation value of ${f ilde{S}}^2-{f ilde{S}}^2_z$ scales with system size at finite temperature

Rigorous finite-temperature conclusions for Hubbard, Kondo lattice, and Anderson models

Use of fluctuation-dissipation theorem and particle-hole transform in derivations

Abstract

Some rigorous conclusions of the Hubbard model, Kondo lattice model and periodic Anderson model at finite temperature are acquired employing the fluctuation-dissipation theorem and particle-hole transform. The main conclusion states that for the three models, the expectation value of ${\bf \tilde{S}}^2-{\bf \tilde{S}}^2_z$ will be of order $N_{\Lambda}$ at any finite temperature.