Long-Range Deformations for Integrable Spin Chains

TL;DR

This paper introduces a recursive method to construct integrable long-range spin chain Hamiltonians from short-range models, elucidating their algebraic structures and applications to supersymmetric gauge theories.

Contribution

It provides a systematic recursive construction of long-range integrable spin chains, including their Bethe equations and deformation parameters, applicable to various symmetry algebras and gauge theories.

Findings

Constructed explicit long-range Hamiltonians from short-range models.

Derived asymptotic Bethe equations for long-range chains.

Established a mapping between long-range and inhomogeneous spin chains.

Abstract

We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary short-range (e.g. nearest-neighbor) integrable spin chains, it allows to construct an infinite set of conserved long-range charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map and dressing phase in the long-range Bethe equations are a result of these deformations. The closed chain asymptotic Bethe equations for long-range spin chains transforming under a generic symmetry algebra are derived. Notably, our construction applies to generalizations of standard nearest-neighbor chains such as alternating spin chains. We also discuss relevant properties for its application to planar D=4, N=4 and D=3, N=6 supersymmetric gauge theories. Finally, we present a map between long-range and inhomogeneous spin chains delivering more insight into the structures of these models as well as their limitations at wrapping order.