Tensor network decompositions in the presence of a global symmetry

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.050301· OSTI ID:21528549

Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre ^[1]

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1. University of Queensland, Department of Physics, Brisbane, Queensland 4072 (Australia)

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.

• OSTI ID: 21528549
• Journal Information: Physical Review. A, Vol. 82, Issue 5; Other Information: DOI: 10.1103/PhysRevA.82.050301; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
COMPUTERIZED SIMULATION
DEGREES OF FREEDOM
INVARIANCE PRINCIPLES
MANY-BODY PROBLEM
QUANTUM GRAVITY
SPIN
SYMMETRY
SYMMETRY GROUPS
TENSORS
ANGULAR MOMENTUM
FIELD THEORIES
MATHEMATICAL LOGIC
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
SIMULATION