New Two-Dimensional Integrable Quantum Models from SUSY Intertwining

TL;DR

This paper explores new two-dimensional integrable quantum models derived from supersymmetry, revealing classes of solutions with unique symmetry properties and applying specialized separation of variables techniques.

Contribution

It introduces novel 2D integrable quantum models from SUSY intertwining with deformed hyperbolic metrics, including solutions with higher-order symmetry operators.

Findings

Found classes of solutions with fourth-order symmetry operators.

Demonstrated models where conventional separation of variables is not possible.

Applied SUSY-based separation techniques to specific models.

Abstract

Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric $g_{ik}=diag(1,-a^2)$. Several classes of particular solutions of these relations are found. The corresponding Hamiltonians do not allow the conventional separation of variables, but they commute with symmetry operators of fourth order in momenta. For some of these models the specific SUSY procedure of separation of variables is applied.