Wrapping corrections for long range spin chains

TL;DR

This paper extends the transfer matrix framework to finite size long range spin chains, enabling the inclusion of wrapping corrections and broadening the understanding of their integrability properties.

Contribution

It generalizes transfer matrices to finite size long range spin chains, incorporating wrapping corrections into their integrable structure.

Findings

Transfer matrices define conserved charges for all chain lengths.

The construction includes wrapping corrections in the spectrum.

Finite size integrable long range spin chains are now well-defined.

Abstract

The long range spin chains play an important role in the gauge/string duality. The aim of this paper is to generalize the recently introduced transfer matrices of integrable medium range spin chains to long range models. These transfer matrices define a large set of conserved charges for every length of the spin chain. These charges agree with the original definition of long range spin chains for infinite length. However, our construction works for every length, providing the definition of integrable finite size long range spin chains whose spectrum already contains the wrapping corrections.