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Recursion relations for long-range integrable spin chains with open boundary conditions

Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark, Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75005 Paris, France, and Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Potsdam, Germany

^*loebbert@nbi.dk

Phys. Rev. D 85, 086008 – Published 25 April, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.086008

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.

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References (19)

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This regularization was also chosen to render the interaction range of periodic long-range charges minimal [9].
We do not identify the operator consisting of two spectator legs according to (7) since it is useful to give the charges a vanishing vacuum eigenvalue.
In [12] the parameters corresponding to even boosts were not yet identified as similarity transformations due to taking different linear combinations of the charges.
This definition of $x (u)$ differs from the one that renders the interaction range of periodic long-range charges minimal [9]. Here $d q_{r} (u) / d α_{k} = 0$ since $γ = 0$ .
G. Arutyunov, S. Frolov, and M. Staudacher, J. High Energy Phys. 10 (2004) 016.
If similarity transformations with the even boosts are switched on, the reflection map $p \to - p$ is deformed by the corresponding parity breaking parameters; cf. [12].

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Recursion relations for long-range integrable spin chains with open boundary conditions

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References (19)

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