The $\beta$-expansion of the $D=1$ fermionic spinless Hubbard model off the half-filling regime

TL;DR

This paper develops a $eta$-expansion method for the Helmholtz free energy of the one-dimensional spinless Hubbard model off half-filling, revealing relations for the chemical potential and extending the expansion to eighth order.

Contribution

It introduces a novel $eta$-expansion approach for the model off half-filling and extends the expansion to eighth order, providing new analytical tools.

Findings

Helmholtz free energy expressed as two $eta$-expansions off half-filling

Chemical potential as a function of temperature satisfies a symmetry relation

Extended $eta$-expansion up to order $eta^8$

Abstract

We found that when the spinless model is off the half-filling regime ($\mu \neq V$), the Helmholtz free energy (HFE) can be written as two $\beta$-expansions: one expansion comes from the half-filling configuration and another one that depends on the parameter $x = \mu - V$. We show numerically that the chemical potential as a function of temperature satisfies a relation similar to the one derived from the particle-hole symmetry of the fermionic spinless model. We extend the $\beta$-expansion of the HFE of the one-dimensional fermionic spinless Hubbard model up to order $\beta^8$.