Patrick Dorey et al 2009 J. Phys. A: Math. Theor. 42 465302 doi:10.1088/1751-8113/42/46/465302
symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
Patrick Dorey1, Clare Dunning2, Anna Lishman1 and Roberto Tateo3
Show affiliationsWe study a three-parameter family of 
-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 Jordan 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 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.
- PACS
- MSC
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81R15 Operator algebra methods (See also 46Lxx, 81T05)
- Subjects
- Dates
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Issue 46 (20 November 2009)
Received 24 July 2009, in final form 10 September 2009
Published 22 October 2009
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symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
Patrick Dorey et al 2009 J. Phys. A: Math. Theor. 42 465302
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