Non-Hermitian Physics on a Curved Surface
Curvature, two-dimensional, bi-orthogonal.
The influence of curved background on the properties of Non-Hermitian (NH) systems is a significant open question
for a broad class of physical applications. We introduce an analytically solvable model of Dirac fermions with imaginary mass
on the sphere. We show the existence of an infinite sequence of exceptional points (EP), which depend on the radius
(curvature) of the sphere. We employ quench dynamics to characterize curvature-dependent NH phase transitions. We
demonstrate that the existence of singular points of the Loschmidt echo and the fidelity are an unambiguous signature of
geometric EPs that distinguish between different phases of the model.