Classification of matrix product ground states corresponding to one dimensional chains of two state sites of nearest neighbor interactions

TL;DR

This paper provides a comprehensive classification of one-dimensional quantum chains with two-state sites and nearest neighbor interactions, identifying all Hamiltonians with matrix product ground states and explicitly constructing them.

Contribution

It offers the first complete classification and explicit construction of Hamiltonians with matrix product ground states for this class of quantum chains.

Findings

Explicit Hamiltonians with matrix product ground states are obtained.

A complete classification of such chains is provided.

The corresponding ground states are explicitly constructed.

Abstract

A complete classification is given for one dimensional chains with nearest neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained.