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Springer series in solid-state sciences

Quantum Transfer-Matrix Method and Its Application to Quantum Spin Systems

Hiroshi Betsuyaku

Published Jan 1, 1987• 3 citations
Publisher
DOI
10.1007/978-3-642-83154-6_5

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Transfer-matrix methods for quantum spin systems are formulated and their limiting properties are studied rigorously. The present formulation is applied explicitly to an exactly soluble transverse Ising model. A computer implementation of the two-dimensional triangular antiferromagnetic quantum Heisenberg model is also proposed to study Anderson's picture of the dynamic coherence of the phase of singlet pairs.

Physical review. B, Condensed matter•Mar 1, 1985•280 citations
An improved transfer matrix method is proposed for calculating the partition function of quantum spin systems, which is expressed by the M-th approximant of the Suzuki-Trotter transformation with Trotter number M. The point is to incorporate the symmetry property of the Trotter subsystem in calculation. The size of our transfer matrix is reduced very much. Thermodynamics is described by the maximum eigenvalue of the transfer matrix. Our method is applied to the XY model with spin 1/2. We consider the cases of pair and tri spin decompositions with Trotter number up to 4 (M≤4). We can do our calculation analytically in those cases. In the pair spin decomposition we find results which have been obtained by the Monte Carlo simulation and by a transfer matrix method by computer. We find nice results in the tri spin decomposition. Our result in the case M=4 is as good as the result in M=8 by the previous Monte Carlo simulation on comparing them with the exact result of Katsura.