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

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We found that when the spinless model is off the half-filling regime (μ≠ V), the Helmholtz free energy (HFE) can be written as two β-expansions: one expansion comes from the half-filling configuration and another one that depends on the parameter x = μ- 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 β-expansion of the HFE of the one-dimensional fermionic spinless Hubbard model up to order β⁸.