On Ground State Degeneracy of $Z_2$ Symmetric Quantum Spin Models

On Ground State Degeneracy of $Z_{2}$ Symmetric Quantum Spin Models

We consider a class of $Z_{2}$ symmetric quantum spin Hamiltonians. Anisotropic spin $1/2$ Heisenberg models are typical examples.

Proof of groound state degeneracy ( $Z_{2}$ symmetry breaking), construction of pure gournd states are given in a systematic way.

Taku Matsui, On Ground State Degeneracy of $Z_{2}$ Symmetric Quantum Spin Models. Publ. Res. Inst. Math. Sci. 27 (1991), no. 4, pp. 657–679