Perturbation theory near degenerate exceptional points

Abstract

In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed. What is assumed is, firstly, that the perturbed Hamiltonians $H=H_0+\lambda V$ are non-Hermitian and lie close to their unobservable exceptional-point (EP) degeneracy limit $H_0$. Secondly, in this EP limit, the geometric multiplicity $L$ of the degenerate unperturbed eigenvalue $E_0$ is assumed, in contrast to the majority of existing studies, larger than one. Under these assumptions the method of construction of the bound states is described. Its specific subtleties are illustrated via the leading-order recipe. The emergence of a counterintuitive connection between the value of $L$, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the EP singularity is given a detailed explanation.

arXiv comment26 pp

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Cited by in corpus (9)

• Symmetry protected exceptional points of interacting fermions
• Paths of unitary access to exceptional points
• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Higher-order exceptional points in composite non-Hermitian systems
• Quantum singularities in a solvable toy model
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Phase transitions in quasi-Hermitian quantum models at exceptional points of order four
• Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model