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

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.

arXiv comment5 pages, 1 figure

References in corpus (3)

• Diverging Entanglement Length in Gapped Quantum Spin Systems
• An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
• An SO(5) Symmetric Ladder

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