Non-Hermitian multi-particle systems from complex root spaces

Abstract

We provide a general construction procedure for antilinearly invariant complex root spaces. The proposed method is generic and may be applied to any Weyl group allowing to take any element of the group as a starting point for the construction. Worked out examples for several specific Weyl groups are presented, focusing especially on those cases for which no solutions were found previously. When applied in the defining relations of models based on root systems this usually leads to non-Hermitian models, which are nonetheless physically viable in a self-consistent sense as they are antilinearly invariant by construction. We discuss new types of Calogero models based on these complex roots. In addition we propose an alternative construction leading to q-deformed roots. We employ the latter type of roots to formulate a new version of affine Toda field theories based on non-simply laced roots systems. These models exhibit on the classical level a strong-weak duality in the coupling constant equivalent to a Lie algebraic duality, which is known for the quantum version of the undeformed case.

29 pages

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Cited by in corpus (7)

• PT-symmetric deformations of integrable models
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• PT-symmetrically deformed shock waves
• $\mathcal{P}\mathcal{T}$ deformation of Calogero-Sutherland models
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Toda field theories and Calogero models associated to infinite Weyl groups
• Non-Hermitian superintegrable systems