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arXiv:1911.12315 · Physical Review Letters

TT¯ Deformations and Integrable Spin Chains

Enrico Marchetto, Alessandro Sfondrini, Zhou Yang

Published Mar 10, 2020• 48 citations
arXivHTMLPDF

Abstract

We consider current-current deformations that generalize TT[over ¯] ones, and show that they may be also introduced for integrable spin chains. In analogy with the integrable QFT setup, we define the deformation as a modification of the S matrix in the Bethe equations. Using results by Bargheer, Beisert and Loebbert we show that the deforming operator is composite and constructed out of two currents on the lattice; its expectation value factorizes like for TT[over ¯]. Such a deformation may be considered for any combination of charges that preserve the model's integrable structure.

DOI
10.1103/physrevlett.124.100601

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We consider current-current deformations that generalize TT[over ¯] ones, and show that they may be also introduced for integrable spin chains. In analogy with the integrable QFT setup, we define the deformation as a modification of the S matrix in the Bethe equations. Using results by Bargheer, Beisert and Loebbert we show that the deforming operator is composite and constructed out of two currents on the lattice; its expectation value factorizes like for TT[over ¯]. Such a deformation may be considered for any combination of charges that preserve the model's integrable structure.
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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.