Conservation laws and integrability of a one-dimensional model of diffusing dimers

We study a model of assisted diffusion of hard-core particles on a line. Our model is a special case of a multispecies exclusion process, but the long-time decay of correlation functions can be qualitatively different from that of the simple exclusion process, depending on initial conditions. This behavior is a consequence of the existence of an infinity of conserved quantities. The configuration space breaks up into an exponentially large number of disconnected sectors whose number and sizes are determined. The decays of autocorrelation functions in different sectors follow from an exact mapping to a model of the diffusion of hard-core random walkers with conserved spins. These are also verified numerically. Within each sector the model is reducible to the Heisenberg model and hence is fully integrable. We discuss additional symmetries of the equivalent quantum Hamiltonian which relate observables in different sectors. We also discuss some implications of the existence of an infinity of conservation laws for a hydrodynamic description