Effect of a magnetic field on the Kitaev model coupled to environment

Open quantum systems can display unusual phenomena not seen in closed systems such as new topological phases and skin effect. An interesting example was studied for the Kitaev model in the previous study [1]. An effective non-Hermitian Kitaev model, which incorporates dissipation effects, was shown to display a new gapless spin liquid state, in which the Dirac-like node in the Hermitian case splits into two exceptional points with square-root dispersions. However, the effect of a magnetic field on the model has not been clarified yet, even though the exceptional points may bring about unprecedented quantum phenomena. In this study, we investigate the effect of a magnetic field on the non-Hermitian Kitaev model based on the perturbation theory. We show that the exceptional points remain gapless up to a nonzero critical field, in stark contrast to the Hermitian case. We also show that the critical field diverges for some particular parameter regions. By calculating the winding number of the exceptional points, we find topological transitions caused by the magnetic field. In addition, in the system with the open boundary condition, we find that the edge states in the skin effect switch from one side to the other through the exceptional points. Our results provide a new possible route to stabilize topological quantum spin liquids under the magnetic field in the presence of dissipation. [1] K. Yang, S. C. Morampudi, and E. J. Bergholtz, Phys. Rev. Lett. 126, 077201 (2021).