2001/09/30 by Tobias J. Osborne, Michael A. Nielsen · 1 citation
Computer Science · Physics and Astronomy · #Density matrix renormalization group #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Reinterpretation #Renormalization #Squashed entanglement #cond-mat #quant-ph
paper · pdf · doi:10.1023/a:1019601218492
published as Quantum Information Processing, vol. 1 (1-2), pp. 45-53 (2002) · 5 pages, 1 eps figure, revtex4; added reference and qualifying remarks
openalex publication_date 2002/04/01 · arxiv created 2002/04/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.