On PT-symmetric extensions of the Calogero and Sutherland models

TL;DR

This paper explores PT-symmetric extensions of the Calogero and Sutherland models, introducing new interactions that preserve integrability and solvability, and also presents a quasi-exactly solvable deformation.

Contribution

It introduces PT-symmetric, non-self-adjoint interactions into Calogero and Sutherland models, revealing new integrable and solvable Hamiltonians and a quasi-exactly solvable deformation.

Findings

Some PT-symmetric interactions preserve integrability.

Certain extensions remain solvable algebraically.

A new quasi-exactly solvable deformation is proposed.

Abstract

The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinus-square potential. They are well known to be integrable and solvable. Here we extend the Calogero and Sutherland Hamiltonians by means of new interactions which are PT-symmetric but not self adjoint. Some of these new interactions lead to integrable PT-symmetric Hamiltonians; the algebraic properties further reveal that they are solvable as well. We also consider PT-symmetric interactions which lead to a new quasi-exactly solvable deformation of the Calogero and Sutherland Hamiltonians.