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

TL;DR

This paper uses matrix product formalism to find exact ground states of two new spin-1 quantum chains, revealing new features and providing explicit correlation functions for these models.

Contribution

It introduces two novel spin-1 quantum chains with exactly solvable ground states and analyzes their properties using matrix product states.

Findings

Exact ground states for two new spin-1 chains found

Correlation functions explicitly calculated

Degeneracy and properties of states analyzed

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 $H=\sum_i ({\bf S}_i\cdot {\bf S}_{i+1})^2$. 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.