arXiv:0901.2223 · Physical Review A

Matrix product states: Symmetries and two-body Hamiltonians

Mikel Sanz, Michael M. Wolf, David Pérez-Garcı́a, J. I. Cirac

Published Apr 6, 2009• 94 citations

Abstract

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)-invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.

DOI: 10.1103/physreva.79.042308

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