Transfer-matrix density-matrix renormalization-group theory for thermodynamics of one-dimensional quantum systems

The transfer-matrix density-matrix renormalization-group method for one-dimensional quantum lattice systems has been developed by considering the symmetry property of the transfer matrix and introducing the asymmetric reduced density matrix. We have evaluated a number of thermodynamic quantities of the anisotropic spin-1/2 Heisenberg model using this method and found that the results agree very accurately with the exact ones. The relative errors for the spin susceptibility are less than ${10}^{-3}$ down to $T=0.01J$ with 80 states kept.