Abstract

A numerical quantum transfer-matrix approach based on the Suzuki-Trotter formula and the checkerbord decomposition is presented in the framework of quantum statistical mechanics. It is applied to the supramolecular cluster Mn₆ (i.e. [Mn(hfac)₂NITPh]₆) and to a number of the macroscopic quasi-one-dimensional magnets. The latter include: (i) the macroscopic Haldane-gap spin S=1 chains and molecular-based magnetic spin S=1 chains (with uniform and alternating interaction couplings); (ii) the spin-Peierls CuGeO₃ and Pb[Cu(SO₄)(OH)₂] compounds subject to frustration; (iii) Yb₄As₃ which is a new semimetallic material being the first example of the antiferromagnetic S=1/2 spin chain with the induced staggered field appearing as a result of the antisymmetric Dzyaloshinsky-Moriya interaction. The compounds in question can be characterized within the spin Heisenberg models and their thermodynamic properties at finite temperatures are calculated using our own codes. Our simulation results are compared with the available experimental results and a quantitative agreement has been established. The large-scale numerical simulations were carried out on the Cray and Silicon Graphics supercomputers, using the parallelized and vectorized codes, exploiting the Parallel Virtual Machine (PVM) and the Message Passing Interface (MPI) system libraries.

Author Keywords: one-dimensional magnets, numerical simulations, quantum transfer-matrix method, Heisenberg model, Dzyaloshinski-Moriya interaction, spin-Peierls transitions

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