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arXiv:cond-mat/0106049 · Modern Physics Letters A

ANGULAR QUANTIZATION AND THE DENSITY MATRIX RENORMALIZATION GROUP

José Gaite

Published Jun 7, 2001• 18 citations
arXivHTMLPDF

Abstract

Path integral techniques for the density matrix of a one-dimensional statistical system near a boundary previously employed in black-hole physics are applied to provide a new interpretation of the density matrix renormalization group: Its efficacy is due to the concentration of quantum states near the boundary.
DOI
10.1142/s0217732301004364

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The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems defined on a chain, an optimal formulation is given by White's ‘density matrix renormalization group’. This formulation can be shown to rely on concepts of the developing theory of quantum information. Furthermore, White's algorithm can be connected with a peculiar type of quantization, namely, angular quantization . This type of quantization arose in connection with quantum gravity problems, in particular, the Unruh effect in the problem of black-hole entropy and Hawking radiation. This connection highlights the importance of quantum system boundaries, regarding the concentration of quantum states on them, and helps us to understand the optimal nature of White's algorithm.
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