A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices

TL;DR

This paper classifies spin-1/2 matrix product states with specific symmetries using two-dimensional auxiliary matrices, identifying three classes and their associated Hamiltonians, including phase transition points and interaction types.

Contribution

It provides a comprehensive classification of such matrix product states, detailing their parent Hamiltonians and quantum phase transition points, which was not previously established.

Findings

Three distinct classes of states identified

Parent Hamiltonians determined for each class

Two models with three-body interactions, one with two-body interaction

Abstract

e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine the parent Hamiltonian and the points of possible quantum phase transitions. For two of the models, the interactions are three-body and for one the interaction is two-body