Tensor network decompositions in the presence of a global symmetry

Singh, Sukhwinder, Pfeifer, Robert N. C. and Vidal, Guifré (2010) Tensor network decompositions in the presence of a global symmetry. Physical Review A - Atomic, Molecular, and Optical Physics, 82 5: 050301-1-050301-4. doi:10.1103/PhysRevA.82.050301

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Author Singh, Sukhwinder
Pfeifer, Robert N. C.
Vidal, Guifré
Title Tensor network decompositions in the presence of a global symmetry
Journal name Physical Review A - Atomic, Molecular, and Optical Physics   Check publisher's open access policy
ISSN 1050-2947
Publication date 2010-11-01
Sub-type Article (original research)
DOI 10.1103/PhysRevA.82.050301
Open Access Status File (Publisher version)
Volume 82
Issue 5
Start page 050301-1
End page 050301-4
Total pages 4
Place of publication College Park, MD, United States
Publisher American Physical Society
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. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research. ©2010 The American Physical Society.
Keyword Computational costs
Degrees of freedom
Global symmetries
Lattice system
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article #050301. Published under Rapid Communications - Quantum information.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
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Citation counts: TR Web of Science Citation Count  Cited 78 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 75 times in Scopus Article | Citations
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Created: Sun, 05 Dec 2010, 10:03:04 EST