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arXiv:cond-mat/9910082 · Springer eBooks

Density Matrix Renormalization

K. Hallberg

Published May 8, 2006• 95 citations
arXivHTMLPDF
DOI
10.1007/0-387-21717-7_1

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The effect of gravity on a two dimensional fluid, or Ising magnet, confined between opposing walls is analyzed by density matrix renormalization. Gravity restores two phase coexistence up to the bulk critical point, in agreement with mean field calculations. A detailed finite size scaling analysis of the critical point shift is performed. Density matrix renormalization results are very accurate and the technique is promising and best suited to study equilibrium properties of two dimensional classical systems in contact with walls or with free surfaces.
The density matrix renormalization group discovered by White is investigated. In the case where renormalization eventually converges to a fixed point we show that quantum states in the thermodynamic limit with periodic boundary conditions can be simply represented by a ``matrix product ground state'' with a natural description of Bloch states of elementary excitations. We then observe that these states can be rederived through a simple variational ansatz making no reference to a renormalization construction. The method is tested on the spin-1 Heisenberg model.