Exact Ground States and Phase Diagram of the Quantum Compass Model Under an In-Plane Field

We have determined the ground-state phase diagram of the square-lattice spin-1/2 quantum compass model (QCM) under an in-plane field using infinite projected entangled pair states. For a special field value, we find that the QCM Hamiltonian may be written in a form such that exact ground states can be identified. The phase surrounding this field value is characterized by a staggered vector chirality order parameter. In the zero-field limit, the QCM is know to have subextensive ground-state degeneracy originating from one-dimensional gauge-like symmetries. We show that this sub-extensive degeneracy is split when finite fields are included in the hamiltonian, and first-order phase transitions are identified. At the edges of the phase diagram, we find phases of weakly-coupled Ising-chain states.