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Quantum Simulation
Matrix Product States: Symmetries and Two-Body Hamiltonians
arXiv
Authors: M. Sanz, M. M. Wolf, D. Perez-Garcia, J. I. Cirac
Year
2009
Paper ID
9266
Status
Preprint
Abstract Read
~2 min
Abstract Words
90
Citations
N/A
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.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations.
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