Exact ground states for two new spin-1 quantum chains, new features of matrix product states

Abstract

We use the matrix product formalism to find exact ground states of two new spin-1 quantum chains with nearest neighbor interactions. One of the models, model I, describes a one-parameter family of quantum chains for which the ground state can be found exactly. In certain limit of the parameter, the Hamiltonian turns into the interesting case $H={\sum }_i({\mathbf{S}}_i\cdot {\mathbf{S}}_{i+1}{)}^2$. The other model which we label as model II, corresponds to a family of solvable three-state vertex models on square two dimensional lattices. The ground state of this model is highly degenerate and the matrix product states is a generating state of such degenerate states. The simple structure of the matrix product state allows us to determine the properties of degenerate states which are otherwise difficult to determine. For both models we find exact expressions for correlation functions.

arXiv comment22 pages, references added, accepted for publication in European Physics Journal B

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• Classification of matrix product ground states corresponding to one dimensional chains of two state sites of nearest neighbor interactions
• A new family of matrix product states with Dzyaloshinski-Moriya interactions