Exactly solvable quantum spin tubes and ladders

We find families of integrable n-leg spin-½ ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to su(N) spin chains with N = 2n. Arbitrary rung interactions in the spin tubes and ladders induce chemical potentials in the equivalent spin chains. The potentials are n-dependent and differ for the tube and ladder models. The models are solvable by means of nested Bethe ansatze.