Finite-lattice expansion for quantum spin chains

Abstract

We investigate the thermal properties of s=1/2 and 1 antiferromagnetic Heisenberg spin chains by an expansion in finite lattices. The expansion is based on expressing the quantity of interest, in the thermodynamic limit, as a sum over contributions from different length scales. The first few terms in the expansion, obtained by diagonalizing chains of length up to 13 for s=1/2 and length up to 9 for s=1, provide an accurate estimate for the internal energy and specific heat for T/J≥0.25 and 0.35, respectively. At lower temperatures, by studying the exponential decay of the various terms in the expansion, we estimate the correlation length ξ. We get good estimates for ξ down to T/J=0.06 for s=1/2 and T/J=0.02 for s=1. We find that for s=1 ξ increases much more slowly than for s=1/2 and is consistent with a value of ξ≊7 at T=0.