Lifting integrable models and long-range interactions

TL;DR

This paper presents a method to verify Yang-Baxter integrability of Hamiltonians and applies it to long-range interactions in N=4 SYM, deriving Lax operators and R-matrices, revealing structural insights at higher loops.

Contribution

It introduces a constructive approach to check integrability and derives explicit Lax operators and R-matrices for long-range models in N=4 SYM.

Findings

All known integrable long-range deformations can be obtained from the method.

Derived Lax operator and R-matrix for the two-loop SU(2) sector.

Discussed structural patterns at higher loops.

Abstract

In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and $R$-matrix of the two-loop SU(2) sector in N=4 SYM. We show that all known integrable long-range deformations of the 6-vertex models of this type can be obtained from a Lax operator and an $R$-matrix. Finally we discuss what happens at higher loops and highlight some general structures that these models seem to exhibit.