superdiffusive transport in chaotic nodal interaction model

Superdiffusive transport in integrable models with non-abelian symmetry has recently attracted significant attention. In this study, we propose a new mechanism to induce superdiffusive transport, which relies on two key elements: (1) a free-fermion Hamiltonian that supports ballistic eigenmodes, and (2) nodal interactions, where the interaction strength vanishes when scattering processes involve quasi-particles with specific momenta k_0, referred to as "nodes." This decoupling between quasi-particles at the nodes and those at other momenta leads to a divergence in the quasi-particle lifetime at the nodes, thereby giving rise to superdiffusion. Through an analysis of the quantum Boltzmann equation, we show that the near-equilibrium dynamics of this model follow a Lévy walk process, with a dynamical exponent given by z=(2n+1)/2n, where n is the order of the node.