Probing hydrodynamic crossovers with dissipation-assisted operator evolution

TL;DR

This paper uses dissipation-assisted operator evolution to study the transition from ballistic to diffusive transport in an interacting lattice model, revealing how diffusion constants depend on charge density.

Contribution

It introduces a generalized DAOE algorithm that reduces operator entanglement and accurately predicts diffusion behavior across various densities.

Findings

Diffusion constant scales as D ∝ 1/ρ at low densities.

The generalized DAOE algorithm effectively approximates non-local operators.

Charge correlation functions match numerical data across densities.

Abstract

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as $D \propto 1/\rho$ at low densities $\rho$. Our numerical approach generalizes the Dissipation-Assisted Operator Evolution (DAOE) algorithm: in the spirit of the BBGKY hierarchy, we effectively approximate non-local operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate predictions for diffusion constants across all density scales. We further construct a minimal model for the transport crossover, yielding charge correlation functions which agree well with our numerical data. Our results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities, and serve as a guide for generalizations to low temperature transport.