Realization of Haldane's Exclusion Statistics in a Model of Electron-Phonon Interactions

We discuss an integrable model describing one-dimensional electrons interacting with two-dimensional anharmonic phonons. In the low temperature limit it is possible to decouple phonons and consider one-dimensional excitations separately. They have a trivial two-body scattering matrix and obey fractional statistics. As far as we know the original model presents the first example of a model with local bare interactions generating purely statistical interactions between renormalized particles. As a by-product we obtain non-trivial thermodynamic equations for the interacting system of two-dimensional phonons.