We present a ``numerically exact'' method to obtain the partition function of one-dimensional quantum systems. The method is suitable for Cray I supercomputers. As an example, for the potential of the method we publish results for random XY and Heisenberg chains.
A simple Monte Carlo high-temperature expansion method to evaluate the partition function of quantum spin systems which was proposed in the previous paper l) is improved so that all of the needed expansion-coefficients are obtained from interpolating points of less than ten with an interpolation formula. By this improvement, this method is applicable to the finite spin-systems of rather large spin size regardless of dimensionality of the system. As an example, the method is applied to the one-dimensional spin-l/2 isotropic Heisenberg ferromagnetic system.
This paper discusses a classical simulation to compute the partition function (or free energy) of generic one-dimensional quantum many-body systems. Many numerical methods have previously been developed to approximately solve one-dimensional quantum systems. However, there exists no exact proof that arbitrary one-dimensional quantum Gibbs states can be efficiently solved by a classical computer. Therefore, the aim of this paper is to prove this with the clustering properties for arbitrary finite temperatures β−1. We explicitly show an efficient algorithm that approximates the partition function up to an error ε with a computational cost that scales as n⋅poly(1/ε), where the degree of the polynomial depends on β as eO(β). Extending the analysis to higher dimensions at high temperatures, we obtain a weaker result for the computational cost n\cdot (1/ε)^{\log^{D-1} (1/ε)}, where D is the lattice dimension.
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