Entanglement Phase Transitions in the Monitored Kitaev Model with Perturbations

Monitored quantum circuits have become a useful tool to explore novel non-equilibrium phases of matter. Recent studies have established a rich phase diagram for the exactly solvable Kitaev honeycomb hamiltonian by taking a stochastic implementation where the two qubit bond operators are chosen for projective measurements with their respective probabilities. These studies have established an area-law phase which is analogous to the gapped phase of the Kitaev hamiltonian, capable of protecting dynamically generated logical qubits for times that scale exponentially with the system size. We now consider the behavior of this measurement-only model under a magnetic field by implementing single qubit projective measurements to model this perturbation. When our bond probabilities are measured uniformly in the presence of a low strength magnetic field, we observe a stabilized, highly entangled volume law phase and when there is a strong bias towards measuring one type of bond, we find a small area law phase that persists for very low field strengths. Further increasing the strength of the magnetic field perturbations leads to a trivial product state phase as these measurements overpower system dynamics and prevent different parts of the system from becoming entangled with one another.