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arXiv:hep-lat/0403008 · Journal of High Energy Physics

Density matrix renormalization group in a two-dimensional 4Hamiltonian lattice model

Takanori Sugihara

Published May 6, 2004• 50 citations
arXivHTMLPDF
DOI
10.1088/1126-6708/2004/05/007

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For quantum spin models defined on a two-dimensional lattice, we look for the best numbering of the lattice sites (a layout) that, at fixed bond dimension and other parameters of the density matrix renormalization group (DMRG) algorithm, gives the lowest value of the variational energy, maximum entropy and truncation error. We consider the conjecture that the optimal layout is a Hamiltonian path, and that it optimizes a simply computable geometric cost function. Finding the minimum of such a function, which is a variant of the minimum linear arrangement problem, provides the DMRG with an efficient layout of the lattice and improves both accuracy and convergence time. We present applications to the antiferromagnetic and spin glass spin-1/2 models on the square and triangular lattices.