Matrix product states: Symmetries and two-body Hamiltonians

By Mikel Sanz, Michael M. Wolf, David Pérez-García, J. I. Cirac. 2009

67 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

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Citations in the corpus

Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, methodology): “As the physical spin transforms according to a half integer representation, the Clebsch Gordan coefficients impose that the virtual irreps alternate between integer and half-integer representations (Sanz et al., 2009b).”
Exploiting matrix symmetries and physical symmetries in matrix product states and tensor trains (2013, background): “Our results are not only intended for a theoretical purpose (similar to [16,20]) but are also interesting for numerical applications (similar to [18,19]).”