Virial Coefficients of the Fermi-Hubbard Model

The Hubbard Model stands as a cornerstone in the study of strongly correlated systems, capturing the intricacies of localized interactions and the effects of the spatially discrete orbitals. In this work we analyze the Fermionic Hubbard Model in the dilute limit. Expanding the Logarithm of the Grand Canonical Partition Function,the Grand Thermodynamic Potential, in a Taylor-series-like expansion of the fugacity with the Virial Coefficients. We compute the Virial Coefficients through obtaining N-body partition functions, and once found we give our results for the Virial Coefficients in the limit of no interaction U=0 to find the non-interacting Virial Coefficients. Then, in the dilute limit we compute the change in the Virial coefficients from the non-interacting case to encapsulate the effects of the on-site interaction. With these results in hand we are empowered to compute the expectations of pressure, the momentum distribution, and density profiles.