A new first-principles method for numerically calculating finite-temperature properties of quantum many-body systems is described. It is used to compute the thermodynamic properties and magnetic correlations of the Hubbard model, with negligible error at temperatures near the bandwidth or above. Results for the half-filled band and a simple cubic or one-dimensional lattice confirm the existence of a high-temperature peak in the specific heat which has been associated with a smooth but rapid change in conductivity. Correlations calculated for the non-half-filled band simple cubic Hubbard model suggest condensation, an entirely unexpected phenomenon whose existence is shown (by unrelated methods) in Paper II.

• Received 22 February 1973

DOI:https://doi.org/10.1103/PhysRevB.10.932