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

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

2008-04-10

arxiv.org/abs/0804.1685v3

J. Phys. A: Math. Theor. 41 (2008) 415201

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages, 1 figure

Scientific paper

10.1088/1751-8113/41/41/415201

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.

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