Simulations of the low-dimensional magnetic systems by the quantum transfer-matrix technique

Abstract

A numerical quantum transfer-matrix approach based on the Suzuki–Trotter formula and the checker-board decomposition is presented in the framework of quantum statistical mechanics. It is applied to the supramolecular cluster Mn 6 (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 CuGeO 3 and Pb[Cu(SO 4)(OH) 2] compounds subject to frustration; (iii) Yb 4As 3 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.