Thermodynamics of the planar Hubbard model

The thermodynamic properties of specific heat, entropy, chemical potential, spin susceptibility ${\chi }_s,$ and charge susceptibility ${\chi }_c$ are studied as functions of temperature and doping within the two-dimensional Hubbard model with various $U/t=4\mathrm{}–12.$ Quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of $4\times 4$ sites. Results show that the entropy at low T reaches a maximum near half-filling at the electron density $n\sim 1\pm 0.15$ in the whole regime of studied $U/t.\mathrm{}$ The pseudogap in ${\chi }_s\mathrm{}\left(T\right)\mathrm{}$ becomes clearly pronounced for $U/t>~8$ while ${\chi }_c$ shows a maximum close to half-filling. The relation of results to those within the $t-J$ model and to experiments is discussed.