Multiple non-Hermitian phase transitions on a quantum torus surface

In this paper, we investigate the emergence of non-Hermitian phase transitions on quantum torus surfaces. We consider a single fermion whose dynamics are governed by the Dirac equation confined to move on a quantum torus surface. The effects of the geometry are taken into account using the tetrad formalism and the spin connection. The Dirac equation gives rise to two coupled first-order differential equations for each spinor component. The eigenvalues and eigenfunctions for each spinor component are computed numerically, and the non-Hermitian phase transitions are investigated in terms of the geometric features of the torus and the magnitude of the imaginary component of the mass.