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Progress of Theoretical Physics Supplement

Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem

Yasuhiro Hieida

Published Jan 1, 2000• 0 citations
Publisher

Abstract

We examined the efficiency of one of the numerical renormalization approaches, which is appropriate for a class of non-equilibrium models. The approach is less consumption of memory and less time for calculation.
DOI
10.1143/ptps.138.590

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The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.