Entanglement, Quantum Phase Transitions, and Density Matrix Renormalization

  • Authors:

  • Tobias J. Osborne;Michael A. Nielsen

  • Affiliations:

  • Department of Mathematics, University of Queensland 4072, Australia. E-mail: tjo@maths.uq.edu.au;Centre for Quantum Computer Technology and Department of Physics, University of Queensland 4072, Australia. E-mail: nielsen@physics.uq.edu.au

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2002

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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.PACS: 03.65.Ud, 73.43.Nq, 05.10.-a