PT-symmetric deformations of integrable models

TL;DR

This paper reviews recent developments in PT-symmetric deformations of integrable models, including quantum spin chains, Calogero-Moser-Sutherland systems, and KdV-type equations, highlighting new non-Hermitian extensions and their physical implications.

Contribution

It introduces novel PT-symmetric deformations of various integrable models, expanding the understanding of non-Hermitian systems in mathematical physics.

Findings

Non-Hermitian quantum spin chains related to minimal conformal field theories

Three types of deformations for Calogero-Moser-Sutherland models

PT-symmetric deformations of KdV-type nonlinear integrable equations

Abstract

We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and non-linear integrable field equations of Korteweg-de-Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models we provide three alternative deformations: A complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real valued field equations of non linear integrable systems and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of KdV-type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.