Entropy and thermopower in the 2D t-J model

The entropy of the two-dimensional $t$-$J$ model is investigated using its 12th order high temperature series. A direct Pad\'{e} extrapolation of the entropy series doesn't converge well for temperatures below $T\sim J$. The series coefficients are exact polynomials so the series convergence can be improved by modifying the series that is extrapolated. By subtracting a scaled version of the series for the entropy of the Heisenberg antiferromagnet from the $t$-$J$ entropy series the low temperature convergence is greatly improved. Using this technique results are obtained for the full range of electron densities and temperatures. The electron density is an adjustable parameter in the series coefficients allowing the density dependence of the entropy and the density derivative at fixed temperature $\partial S/\partial n|_T$ to be determined accurately. The density derivative depends strongly on temperature, unlike noninteracting models. The density derivative is also an approximation to the experimentally measured thermopower.