Families of commuting transfer matrices and integrable models with disorder

A family of commuting transfer matrices is shown to be associated to each symmetry transformation of a given Yang-Baxter algebra. This applies in lattices models and field theory. The Yang-Baxter algebra remains unchanged when an arbitrary parameter μsub(l) is associated to each lattice site. We generate in this way integrable one-dimensional hamiltonians with long-range couplings and disorder given by the [μsub(l)]. These operators are lattice versions of the non-local charges in sigma models. As a simple example we get a Dzialozhinski-Moriya interaction with an arbitrary coupling per site from the six-vertex model. A similar model with a disordered magnetic field follows too. Their exact solution by an algebraic Bethe ansatz is presented. We derive the excitations spectrum in terms of the density of parameters rho(μ). As another application, the total spin S2 is computed for a XXZ Heisenberg chain (μsub(l)identical0) as a function of the anisotropy Δ (-infinite<Δ<+infinite). (orig.)