Tensor network states and algorithms in the presence of a global SU(2) symmetry

By Sukhwinder Singh, R. Pfeifer, Guifré Vidal. 2010

242 citations recorded by the source corpus.

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. APLRAAN1050-294710.1103/ PhysRevA.82.050301 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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ee9ef746f2715e8db8f95320fe2056dc89f8018a

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Nuclear and High Energy Physics

Citations in the corpus

The density matrix renormalization group for ab initio quantum chemistry (2014, methodology): “This opened the path to implement multiplicity-free non-Abelian symmetries also in TNSs [164–166].”
Stripe order in the underdoped region of the two-dimensional Hubbard model (2016, methodology): “To increase the efficiency we make use of Abelian symmetries (64, 65).”
Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) (2018, background): “the basic idea is that we can ensure a block structure of each tensor individually. One can argue based on representation theory of groups that the tensors can be decomposed in such a block structure [14,15]. However, here we present a bottom-up approach which is closer to the implementation. Motiva”