Entanglement, quantum phase transitions, and density matrix renormalization
arXiv:quant-ph/0109024 · doi:10.1023/A:1019601218492
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.
5 pages, 1 eps figure, revtex4; added reference and qualifying remarks
References in corpus (6)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Mixed State Entanglement and Quantum Error Correction
- Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
- Approximate transformations and robust manipulation of bipartite pure state entanglement
- Quantum information and physics: some future directions
- Entanglement and thermodynamical analogies
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- Entanglement-Entropy for Groundstates, Low-lying and Highly Excited Eigenstates of General (Lattice) Hamiltonians
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- Complexity and quenches in models with three and four spin interactions
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- Entanglement Entropy and The Density Matrix Renormalization Group
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- Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
- Quantum Decimation in Hilbert Space: Coarse-Graining without Structure
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- Renormalization Group and Quantum Information
- Multipartite quantum correlations in a two-mode Dicke model
- Rethinking Renormalization for Quantum Phase Transitions
- Introduction to quantum information theory and outline of two applications to physics: the black hole information paradox and the renormalization group information flow
- Entanglement and separability of quantum harmonic oscillator systems at finite temperature
- Equally entangled multiqubit states
- Data compression limit for an information source of interacting qubits