Pressure, Negative Thermal Expansion and d-wave Pair Fluctuations in the 2D t-J Model

The high temperature series for the entropy of the 2D t-J model has been calculated to 12th order in β. Extrapolating this series below T≤ J has proven difficult in the past due to the presence of two temperature scales. Using a calculation of the Heisenberg AF entropy¹ a modified series for the entropy per site S of the t-J model can be produced ΔS(n,T) = S_tJ(n,T) - nS_AF(J^*). By adjusting J^* the series for ΔS can be extrapolated to lower temperatures using Pade approximants. This can be done for any density and allows the calculation of ∂S/∂n│_T. Using standard thermodynamics the temperature derivative of the pressure ∂P/∂T│_n = -n∂S/∂n│_T + S can be found, along with the full pressure P by integrating ∂P/∂T│_n and using the known high temperaure values. There is a range of densities and temperatures where ∂P/∂T│_n < 0. This region has a strong overlap with the model parameters where the strongest d-wave pair fluctuations² are found. Since ∂P/∂T│_n = α/κ, where α is the thermal expansion coefficient and κ ≥ 0 is the isothermal compressibility, the strongest d-wave pair fluctuations are found where the t-J model has a negative electronic thermal expansion.

1. W. O. Putikka, J. Phys.: Conf. Series 640, 012046 (2015).
2. W. O. Putikka, M. U. Luchini, PRL 96, 247001 (2006).