On ground state degeneracy of \(\mathbb{Z}_ 2\) symmetric quantum spin models
For a class of \(\mathbb{Z}_ 2\) symmetric quantum spin Hamiltonians the proof of the ground state degeneracy is presented and the construction of pure ground states is given. First, the finite volume ground state (which is unique) is described. Then the representations of the algebra of observables on \(L^ 2\) space of Gibbs measure are studied. The states constructed are related to ground state representation. The Markov semigroup and the existence of mass gap are discussed. Finally, Heisenberg models of spin one half are considered as examples.
scientific article; zbMATH DE number 55938