Abstract
We show that the theoretical framework linking exceptional points (EPs) to phase transitions in parity-time (PT) symmetric Hamiltonians is incomplete. Particularly, we demonstrate that the application of the squaring operator to a Jx PT lattice dramatically alter the topology of its Riemann surface, eventually resulting in a system that can cross an EP without undergoing a symmetry breaking. We elucidate on these rather surprising results by invoking the notion of phase diagrams in higher dimensional parameter space. Within this perspective, the canonical PT symmetry breaking paradigm arises only along certainprojections of the Riemann surface in the parameter space.
Highlights
Exceptional points (EPs) are peculiar singularities associated with multivalued complex function[1]
What is surprising though, is the lack of any rigorous mathematical proof for this statement. We show that this is not a coincidence, and that this widely accepted picture of PT phase transition is incomplete
We briefly review the archetypal discrete PT-symmetric Hamiltonian, which was the subject of detailed investigation in several studies[7,9,10,15,16]
Summary
Exceptional points (EPs) are peculiar singularities associated with multivalued complex function[1]. We use the squaring operator to construct a simple Hamiltonian that violates the canonical PT phase transition in the following sense: as one parameter is varied continuously and monotonically along a straight line, the system crosses an EP without any PT symmetry breaking.
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