Long-Range Deformations for Integrable Spin Chains

Details Long-Range Deformations for Integrable Spin Chains Long-Range Deformations for Integrable Spin Chains

2009-02-05

arxiv.org/abs/0902.0956v2

J.Phys.A42:285205,2009

Physics

High Energy Physics

High Energy Physics - Theory

63 pages, v2: references added

Scientific paper

10.1088/1751-8113/42/28/285205

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.

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