Superdiffusive transport in chaotic quantum systems with nodal interactions

Abstract

We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength $\omega (q)\sim q^z$ with dynamical exponent $z=\min [(2n+d)/2n,2]$, where $n$ is the order of the nodal point in momentum space. We verify our predictions in one dimensional systems using tensor-network techniques.

10 pages, 2 figures

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