Temperature-driven crossover phenomena in the correlation lengths of the one-dimensional -J model

We describe a modified transfer matrix renormalization group (TMRG) algorithm and apply it to calculate thermodynamic properties of the one-dimensional t − J model. At the supersymmetric point we compare with Bethe ansatz results and make direct connection to conformal field theory (CFT). In particular we study the crossover from the non-universal high- T lattice into the quantum critical regime by calculating various correlation lengths and static correlation functions. Finally, the existence of a spin-gap phase is confirmed.