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

Tu, Hong-Hao; Zhang, Guang-Ming; Xiang, Tao

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

Authors

Tu, Hong-Hao

Zhang, Guang-Ming

Xiang, Tao

Description

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.
5 pages, 1 figure