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Computational Methods in Science and Technology

ALGORITHM FOR CALCULATION OF THE PARTITION FUNCTION OF FRUSTRATED S = 1/2 HEISENBERG CHAINS

G. Szukowski, M. Bieliński, G. Kamieniarz

Published Jan 1, 2002• 0 citations
Publisher

Abstract

The paper presents the algorithm for calculation of the maximum eigenvalue of the transfer matrix for one-dimensional S=1/2 Heisenberg model with nearest and next-nearest neighbours interactions.This value permits a calculation of the partition function and free energy of the quantum system.This algorithm is implemented in the mevnnn procedure written in FORTRAN 90.The procedure is available at the Poznań Supercomputing and Networking Center on Cray T3E supercomputer in the library /usr/local/lib/libms.a

DOI
10.12921/cmst.2002.08.01.97-101

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The paper presents the algorithm for calculation of the maximum eigenvalue of the transfer matrix for one-dimensional S=1/2 Heisenberg model with nearest and next-nearest neighbours interactions.This value permits a calculation of the partition function and free energy of the quantum system.This algorithm is implemented in the mevnnn procedure written in FORTRAN 90.The procedure is available at the Poznań Supercomputing and Networking Center on Cray T3E supercomputer in the library /usr/local/lib/libms.a
The one-dimensional S=1 quantum spin system has been mapped onto the equivalent two-dimensional Ising model on the basis of the equivalence theorem of Suzuki. The classical representation of the partition function has been expressed in terms of the maximum eigenvalue of the transfer matrix and evaluated by means of the numerically exact transfer-matrix method. The physical meaning of two kinds of correlation functions in RSD and CBD has been made clear in terms of the concept of the maximum eigenstate. Calculations have been made for both ferromagnetic and antiferromagnetic Heisenberg chains with several single-site anisotropy values, both positive and negative. Good agreements are found with some existing numerical results.