Tensor network states and algorithms in the presence of a global U(1) symmetry

Singh, Sukhwinder, Pfeifer, Robert N. C. and Vidal, Guifre (2011) Tensor network states and algorithms in the presence of a global U(1) symmetry. Physical Review B, 83 11: . doi:10.1103/PhysRevB.83.115125

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Author Singh, Sukhwinder
Pfeifer, Robert N. C.
Vidal, Guifre
Title Tensor network states and algorithms in the presence of a global U(1) symmetry
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
Publication date 2011-03
Sub-type Article (original research)
DOI 10.1103/PhysRevB.83.115125
Open Access Status File (Publisher version)
Volume 83
Issue 11
Total pages 22
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2012
Language eng
Formatted abstract
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper Phys. Rev. A 82 050301 (2010) we discussed how to incorporate a global internal symmetry, given by a compact, completely reducible group G, into tensor network decompositions and algorithms. Here we specialize to the case of Abelian groups and, for concreteness, to a U(1) symmetry, associated, e.g., with particle number conservation. We consider tensor networks made of tensors that are invariant (or covariant) under the symmetry, and explain how to decompose and manipulate such tensors in order to exploit their symmetry. In numerical calculations, the use of U(1)-symmetric tensors allows selection of a specific number of particles, ensures the exact preservation of particle number, and significantly reduces computational costs. We illustrate all these points in the context of the multiscale entanglement renormalization Ansatz.
Keyword Density matrix renormalization
Quantum spin chains
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
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Citation counts: TR Web of Science Citation Count  Cited 47 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 30 times in Scopus Article | Citations
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Created: Sun, 11 Sep 2011, 05:17:36 EST by System User on behalf of Physics