Recursion Relations for Long-Range Integrable Spin Chains with Open Boundary Conditions

TL;DR

This paper develops recursion relations to generate integrable charges for open long-range spin chains, extending methods used for short-range and periodic models, with implications for gauge/gravity duality.

Contribution

It introduces a novel recursive framework for constructing integrable charges in open long-range spin chains, bridging short-range models and long-range integrable systems.

Findings

Recursion relations successfully generate long-range integrable charges for open chains.

Framework extends existing methods from short-range to long-range models.

Potential applications in gauge/gravity correspondence and quantum integrability.

Abstract

It is well known that integrable charges for short-range (e.g. nearest-neighbor) spin chains with periodic boundary conditions can be recursively generated by a so-called boost operator. In the past, this iterative construction has been generalized to periodic long-range spin chains as they appear in the context of the gauge/gravity correspondence. Here we introduce recursion relations for open long-range spin chain charges converting a short-range into a long-range integrable model.