Abstract
We propose a matrix product state (MPS) formulation to calculate thermodynamic quantities of one dimensional (1D) quantum systems. The maximum-eigenvalue eigenstate of the quantum transfer matrix is represented as the product of local matrices, which are obtained by the DMRG method for the two dimensional (2D) classical system mapped from the original 1D quantum system. This MPS formulation is successfully applied to the S = ½ XY model.
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