| We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems, relying on a semi-infinite chain coupled to an endpoint impurity as a prototype model. We outline our method to locate the EPs in such systems and carry this out for our prototype, further obtaining an eigenvalue expansion in the vicinity of the EPs that gives rise to characteristic exponents. Finally, we offer a heuristic QPT analogy for the emergence of the resonance (giving rise to broken time symmetry via exponential decay) in which the decay width plays the role of the order parameter; the associated critical exponent is then determined by the eigenvalue expansion in the vicinity of the EP. |
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