  We study integrable models in the context of the recently discovered
Gauge/YBE correspondence, where the Yang-Baxter equation is promoted to a
duality between two supersymmetric gauge theories. We study flavored elliptic
genus of 2d $\mathcal{N}=(2,2)$ quiver gauge theories, which theories are
defined from statistical lattices regarded as quiver diagrams. Our R-matrices
are written in terms of theta functions, and simplifies considerably when the
gauge groups at the quiver nodes are Abelian. We also discuss the modularity
properties of the R-matrix, reduction of 2d index to 1d Witten index, and
string theory realizations of our theories.
