Exact properties of the chemical potential-density relation at finite temperature in the Hubbard model

TL;DR

This paper rigorously analyzes the chemical potential-density relation in the Hubbard model at finite temperature, revealing symmetry-based properties and exact expressions in specific limits.

Contribution

It provides new rigorous insights into the functional properties of the chemical potential-density relation in the Hubbard model, including symmetry considerations and exact limiting cases.

Findings

Charge susceptibility reaches a local extremum at half-filling

Exact expressions derived for two limiting cases

Symmetry considerations inform the properties of the $-$ relation

Abstract

We draw some rigorous conclusions about the functional properties of the $\mu-\rho$ relation in the Hubbard model based on symmetry considerations and unitary transformations. It is shown that the charge susceptibility reaches its local extreme at half-filling. Exact expressions are obtained in two limiting cases.