From the Bethe Ansatz to the Gessel-Viennot theorem (Q1306598)

The authors prove the equivalence of the so-called Bethe Ansatz [see, e.g., \textit{E. H. Lieb}, Phys. Rev. 162, 162-172 (1967)] for the eigenvectors of transfer matrices in a generalized inhomogeneous five-vertex model on the square lattice, to the Gessel-Viennot determinants [cf. \textit{I. M. Gessel} and \textit{G. Viennot}, Adv. Math. 58, 300-321 (1985; Zbl 0579.05004)] for the number of configurations of non-intersecting directed lattice paths (vicious walkers). The theorems can be generalized to any regular planar lattice.