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

Understand

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.