Spontaneous symmetry breakings in \(\mathbb{Z}_{2}\) gauge theories for doped quantum dimer and eight-vertex models (Q1775559)

The authors study Ising gauge theory (IGT) coupled with fermions. In particular in the strong-coupling region the behaviour of the charge and spin degrees of freedom of fermions is investigated. It is shown that in the even IGT the superconducting state is realized, where as in the odd IGT Neél state appears. This result is applied to the quantum dimer model on the square lattice. In the valence-bound crystal phase a dimer or Neél like states of the fermions spin degrees of freedom appears. Further the doped quantum eight-vertex (q8v) model is considered. It is shown that in the ordered state of the q8v model the doped fermions are in the superconducting phase, where as in the topologically ordered phase low-energy excitations are weakly interacting fermions.