Renormalization group and quantum information

Abstract

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.

Low-energy properties of non-perturbative quantum systems: A space reduction approach

“…It can be applied to all types of microscopic quantum systems (molecular, atomic, nuclear, solid state,...) in contradistinction with more specific procedures such as f.i. the Density Matrix Renormalization Group (DMRG) [11,12,13,7] which are more specifically applied to systems which live on a lattice. The reduction concept shows some connection with the method which has been proposed and applied in problems related to the treatment of phonons [6,8] by means of an efficient method which connects a density matrix approach with optimized space dimension reduction.…”