Unified renormalization-group approach to the thermodynamic and ground-state properties of quantum lattice systems

It is shown that some recently proposed iterative approaches to the ground state of quantum systems can be obtained as zero-temperature limits of free-energy-preserving renormalization transformations, if the perturbative expansion is handled in the appropriate way. Besides giving new insight into the ground-state approaches and their mutual relationships, these results allow us to perform consistent approximate calculations of the free energy at all temperatures and to get global descriptions of the critical properties. Free-energy and specific-heat calculations are reported for XY and Heisenberg spin- chains and for the triangular XY model. It is also demonstrated how this extension into finite temperatures allows us to compute in a consistent way the z exponent, and to obtain substantial improvement in the numerical values for the ground-state energy density of the transverse Ising model.