  Non-Hermitian systems with aperiodic order display phase transitions that are
beyond the paradigm of Hermitian physics. Unfortunately, owing to the
incommensurability of the potential most of known non-Hermitian models are not
integrable. This motivates the search for exactly solvable models, where
localization/delocalization phase transitions, mobility edges in complex plane
and their topological nature can be unraveled. Here we present an exactly
solvable model of quasi crystal, which is a non-pertrurbative non-Hermitian
extension of a famous integrable model of quantum chaos proposed by Grempel
{\it at al.} [Phys. Rev. Lett. {\bf 49}, 833 (1982)] and dubbed the Maryland
model. Contrary to the Hermitian Maryland model, its non-Hermitian extension
shows a richer scenario, with a localization-delocalization phase transition
via topological mobility edges in complex energy plane.
