PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials

Abstract

We study a three-parameter family of PT-symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corresponding Jordon block structures by exploiting the quasi-exact solvability of a subset of the models. The mapping of the phase diagram is completed using a combination of numerical, analytical and perturbative approaches. Among other things this reveals some novel properties of the Bender-Dunne polynomials, and gives a new insight into a phase transition to infinitely-many complex eigenvalues that was first observed by Bender and Boettcher. A new exactly-solvable limit, the inhomogeneous complex square well, is also identified.

arXiv comment42 pages, many figures

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Cited by in corpus (5)

• From PT-symmetric quantum mechanics to conformal field theory
• The Bethe Ansatz and the Tzitzéica-Bullough-Dodd equation
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Exceptional points and pseudo-Hermiticity in real potential scattering
• Spectral zeta functions of a 1D Schrödinger problem