The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Entanglement Renormalization
Open accessAbstract
We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.
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Cites
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
The renormalization group: Critical phenomena and the Kondo problem
Wilson, K. G. (1975) · Reviews of Modern Physics · doi:10.1103/revmodphys.47.773 · Cited by 4,522
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
Density-matrix algorithms for quantum renormalization groups
White, S. R. (1993) · Physical Review B · doi:10.1103/physrevb.48.10345 · Cited by 3,244
Entanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793
Self-citationEfficient Classical Simulation of Slightly Entangled Quantum Computations
Vidal, G. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.147902 · Cited by 2,368
Self-citationEfficient Simulation of One-Dimensional Quantum Many-Body Systems
Vidal, G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.040502 · Cited by 1,779
Self-citationScaling laws for ising models near Tc
Kadanoff, L. P. (1966) · Physics Physique Fizika · doi:10.1103/physicsphysiquefizika.2.263 · Cited by 1,608
Finitely correlated states on quantum spin chains
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099178 · Cited by 1,422
Real-Time Evolution Using the Density Matrix Renormalization Group
White, S. R., & Feiguin, A. E. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.076401 · Cited by 1,398
Research works printed but not linked: 1
- P. Calabrese, 2004, J. Stat. Mech., 0406, P002
Cited by
Colloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
Entanglement entropy and conformal field theory
Calabrese, P., & Cardy, J. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504005 · Cited by 1,688
“le like 1/logχ. It is worth mentioning that a new numerical algorithm specifically based on the scaling properties of the entanglement in a conformal critical point has been recently proposed by Vidal [110]: the multi-scale entanglement renormalization ansatz (MERA). In a MERA, the ground-state of an extended quantum s…”
MethodSymmetry protected topological orders and the group cohomology of their symmetry group
Chen, X., Gu, Z.-C., Liu, Z.-X., & Wen, X.-G. (2013) · Physical Review B · doi:10.1103/physrevb.87.155114 · Cited by 1,311
Entanglement renormalization and holography
Swingle, B. (2012) · Physical Review D · doi:10.1103/physrevd.86.065007 · Cited by 915
Metadata
- Authors
- Vidal, G.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-11-28
- Volume
- 99
- Issue
- 22
- Pages
- 220405-220405
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3037108023
- Cited by
- 1,122
- References
- 15
- FWCI
- 20.57
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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