Journal
PHYSICAL REVIEW A
Volume 79, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.79.042308
Keywords
Hilbert spaces; many-body problems; spin Hamiltonians; SU(2) theory; symmetry; tensors
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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.
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