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

Understand

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 [arXiv:0907.2994v1] 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, often associated 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.