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

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...

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Bibliographic Details
Published in:arXiv.org 2009-07
Main Authors: Dorey, Patrick, Dunning, Clare, Lishman, Anna, Tateo, Roberto
Format: Article
Language:English
Subjects:
Broken symmetry
Eigenvalues
Hamiltonian functions
Mapping
Mathematical models
Phase diagrams
Phase transitions
Polynomials
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0907.3673