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.

14 pages, 5 figures, to appear in Phys. Rev. B