Two temperature scales in the d-wave pair correlation length of the 2D t-J model

Two temperature scales are observed in the d-wave pair correlation length for doping $\delta\sim0.25$. Both the s-wave and d-wave pair correlation lengths increase with decreasing temperature starting at very high temperatures. By $T\sim3J$ both symmetries have grown to $\sim1/3$ of a lattice spacing. For $T>3J$ the s-wave correlation length is a few percent larger than d-wave. At $T\sim3J$ both symmetries are saturating, with the growth in the correlation length flattening for both symmetries. The s-wave correlation length does not grow at lower temperatures. The d-wave correlation length does resume growing at $T\sim0.8J$, with the growth at low temperatures much stronger than it was at high temperatures. The d-wave correlation length reaches a size of one lattice spacing at $T\sim0.25J$ with no sign of saturating. Interestingly, both of these temperature scales also occur in the t-J model momentum distribution $n_{\bf k}$. The features that are found in the temperature dependence of the 2D $n_{\bf k}$ on the zone diagonal are very similar to the temperature dependence of the 1D t-J model $n_{\bf k}$. These observations can be understood by having spin-charge separated degrees of freedom.