Superdiffusive transport in chaotic quantum systems with nodal interactions

TL;DR

This paper introduces a class of chaotic fermionic quantum models with nodal interactions that exhibit superdiffusive transport, characterized by long-lived quasiparticles and anomalous dispersion relations, verified through tensor-network simulations.

Contribution

It demonstrates that nodal interactions induce superdiffusive transport and long-lived quasiparticles in chaotic quantum systems, with a non-perturbative analysis and tensor-network verification.

Findings

Diverging diffusion constant due to nodal structure

Anomalous dispersion relation with dynamical exponent z

Verification in 1D systems using tensor networks

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 $z={\rm min}[(2n+d)/2n,2]$, where $n$ is the order of the nodal point in momentum space. We verify our predictions in one dimensional systems using tensor-network techniques.