Quantum decimation for spin-(1/2) chains in a magnetic field

We have extended the range of application of the decimation renormalization-group (RG) method, using a combination of analytic and numerical techniques in calculating thermal and magnetic properties of a wide variety of one-dimensional quantum spin-(1/2) systems. Efforts to improve the accuracy of the approach include increasing the spatial rescaling factor and investigating the effect of free versus periodic boundary conditions for each renormalization cluster. We have used the RG method to calculate the specific heat and susceptibility for chains with uniaxial exchange anisotropy (ranging from the Ising to the XY limits) in both longitudinal and transverse magnetic fields, as well as for the Heisenberg antiferromagnet with alternating couplings, and have compared our results, when possible, with either exact solutions or with numerical extrapolations from finite-chain calculations. Decimation is a high-temperature approximation, but its range of reliability is found in some cases (e.g., transverse susceptibility for the Ising chain, or susceptibility for the Heisenberg ferromagnet in a field) to extend well into the strong-coupling regime. We note that the decimation results for magnetic properties are, in general, more accurate than those for the thermal response.