Paths of unitary access to exceptional points

TL;DR

This paper revisits the concept of exceptional points in quantum systems, arguing that their perceived inaccessibility is due to misinterpretations, and demonstrates this with perturbed Bose-Hubbard models.

Contribution

It clarifies the conditions under which exceptional points can be accessed in unitary quantum systems, challenging previous notions of their fragility.

Findings

Exceptional points can be accessed in unitary quantum systems under certain conditions.

Misinterpretations of quasi-Hermitian theory led to the belief in fragility of EPs.

Perturbed Bose-Hubbard models illustrate the feasibility of accessing EPs.

Abstract

During the early history of unitary quantum theory the Kato's exceptional points (EPs, a.k.a. non-Hermitian degeneracies) of Hamiltonians $H(\lambda)$ did not play any significant role, mainly due to the Stone theorem which firmly connected the unitarity with the Hermiticity. During the recent wave of optimism people started believing that the corridors of a unitary access to the EPs could be opened leading, say, to a new picture of quantum phase transitions via an {\it ad hoc} weakening of the Hermiticty (replaced by the quasi-Hermiticity). Subsequently, the pessimism prevailed (the paths of access appeared to be fragile). In a way restricted to the quantum physics of closed systems a return to optimism is advocated here: the apparent fragility of the corridors is claimed to follow from a misinterpretation of the theory in its quasi-Hermitian formulation. Several perturbed versions of the realistic many-body Bose-Hubbard model are chosen for illustration purposes.