$T\bar{T}$ deformations and integrable spin chains

We consider current-current deformations that generalise $T\bar{T}$ 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 factorises like for $T\bar{T}$. Such a deformation may be considered for any combination of charges that preserve the model's integrable structure.