Probing non-Hermitian phase transitions in curved space via quench dynamics

Non-Hermitian Hamiltonians are relevant to describe the features of a broad class of physical phenomena, ranging from photonics and atomic and molecular systems to nuclear physics and mesoscopic electronic systems. An important question relies on the understanding of the influence of curved background on the static and dynamical properties of non-Hermitian systems. In this work, we study the interplay of geometry and non-Hermitian dynamics by unveiling the existence of curvature-dependent non-Hermitian phase transitions. We investigate a prototypical model of Dirac fermions on a sphere with an imaginary mass term. This exactly-solvable model admits an infinite set of curvature-dependent pseudo-Landau levels. We characterize these phases by computing an order parameter given by the pseudo-magnetization and, independently, the non-Hermitian fidelity susceptibility. Finally, we probe the non-Hermitian phase transitions by computing the (generalized) Loschmidt echo and the dynamical fidelity after a quantum quench of the imaginary mass and find singularities in correspondence of exceptional radii of the sphere.