Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states

Abstract

We introduce a class of exactly solvable SO(n) symmetric Hamiltonians with matrix product ground states. For an odd $n\ge 3$ case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even $n\ge 4$ case, the ground state is a spontaneously dimerized state with twofold degeneracy. In the matrix product ground states for both cases, we identify a hidden antiferromagnetic order, which is characterized by nonlocal string order parameters. The ground-state phase diagram of a generalized SO(n) symmetric bilinear-biquadratic model is discussed.

11 pages, 5 figures

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