String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states

TL;DR

This paper introduces exactly solvable Hamiltonians with SO(2n+1) symmetry whose ground states are matrix product states exhibiting hidden topological order, characterized by nonlocal string order parameters and a hidden $(Z_{2}\times Z_{2})^{n}$ symmetry.

Contribution

The work constructs new exactly solvable models with SO(2n+1) symmetry, revealing their hidden topological order and symmetry-breaking properties in matrix product states.

Findings

Identification of hidden topological order via string order parameters

Ground state degeneracy related to symmetry breaking

Application of these states to measurement-based quantum computation

Abstract

We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and characterized by a set of nonlocal string order parameters. The Hamiltonian possesses a hidden $(Z_{2}\times Z_{2})^{n} $ topological symmetry. The breaking of this hidden symmetry leads to $4^{n}$ degenerate ground states with disentangled edge states in an open chain system. Such matrix product states can be regarded as cluster states, applicable to measurement-based quantum computation.