Lifting integrable models and long-range interactions

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.

21 pages, v2: added two references, minor corrections, v3: added few comments, minor corrections

References in corpus (8)

• Constructing Integrable Lindblad Superoperators
• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Yang-Baxter and the Boost: splitting the difference
• Classifying nearest-neighbour interactions and deformations of AdS
• Integrable quantum spin chains with free fermionic and parafermionic spectrum
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Wrapping corrections for long range spin chains
• Spin chains with boundary inhomogeneities

Cited by in corpus (2)

• The deformed Inozemtsev spin chain
• Integrable models on Rydberg atom chains