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Class of exactly solvable<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>symmetric spin chains with matrix product ground states
We introduce a class of exactly solvable $SO(n)$ symmetric Hamiltonians with matrix product ground states. For an odd $n\ensuremath{\ge}3$ case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even $n\ensuremath{\ge}4$ case, the ground state is a spontaneously dimerized state with twofold degeneracy. In …