Ja n 20 03 Entanglement Entropy and The Density Matrix Renormalization Group

Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a “geometric entropy”, associated with an event horizon as a boundary that concentrates a large number of quantum states. This allows one to connect with the “density matrix renormalization group” and to unveil its connection with the theory of quantum information. This renormalization group has been introduced in condensed matter physics in a heuristic manner, but it can be conceived as a method of compression of quantum information in the presence of a horizon. We propose generalizations to problems of interest in cosmology. 1 Entanglement entropy in some relevant geometries Entanglement or nonseparability refers to the existence of quantum correlations between two sets of degrees of freedom of a physical system that can be considered as subsystems. It is natural that two (sub)systems in interaction are entangled an that they still are entangled after their interaction has ceased. Particularly interesting situations arise when two entangled systems become causally disconnected because of an event horizon. 1.