Cluster Transfer-Matrix Method for One-Dimensional Quantum Spin Systems : Condensed Matter and Statistical Physics

概要

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A formulation is given to map the one-dimensional S=1/2 quantum spin systems onto the two-dimensional Ising model with many-spin interactions on the basis of the n-spin cluster decomposition (n CLD). The cluster transfer matrix is defined which characterizes the thermodynamical properties of the equivalent system. A prescription is presented to construct the cluster transfer matrix and to evaluate its maximum eigenvalue numerically. The method has been applied to the calculation of the energy and specific heat of the XY model for various values of the cluster size n and the Trotter size m. The convergence properties of the energy as a function of n and m have been studied in detail. The main results obtained are:(1) The low-temperature behavior is improved much more by considering larger spin clusters; (2) the energy depends on the spin cluster through the effective cluster size n_e defined by n_e=(n+1)/2; and (3) the energy converges linearly with 1/n_e^2m^2 except at very low temperatures.
理論物理学刊行会の論文
1986-04-25