Entanglement, quantum phase transitions, and density matrix renormalization

authored by

Tobias J. Osborne, Michael A. Nielsen

Abstract

We investigate the role of entanglement in quantum phase transitions, and show that the success of the density matrix renormalization group (DMRG) in understanding such phase transitions is due to the way it preserves entanglement under renormalization. We provide a reinterpretation of the DMRG in terms of the language and tools of quantum information science which allows us to rederive the DMRG in a physically transparent way. Motivated by our reinterpretation we suggest a modification of the DMRG which manifestly takes account of the entanglement in a quantum system. This modified renormalization scheme is shown,in certain special cases, to preserve more entanglement in a quantum system than traditional numerical renormalization methods.

External Organisation(s)

University of Queensland

Type

Article

Journal

Quantum Information Processing

Volume

1

Pages

45 - 53

ISSN

1570-0755

Publication date

04.2001

Publication status

Published

Electronic version(s)

https://doi.org/10.1023/A:1019601218492 (Access: Unknown)