Dissipation-assisted operator evolution method for capturing hydrodynamic transport

TL;DR

The paper presents the DAOE method, which uses artificial dissipation to efficiently compute long-time transport properties in strongly interacting lattice systems, enabling accurate estimation of diffusion constants.

Contribution

The paper introduces the DAOE method that employs dissipation to reduce operator entanglement, allowing for long-time dynamics calculation in strongly interacting systems.

Findings

Successfully computes spin and energy diffusion constants.

Dissipation reduces operator entanglement, enabling long-time simulations.

Extrapolation to zero dissipation yields high-precision physical diffusion constants.

Abstract

We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. DAOE is based on evolving observables in the Heisenberg picture, and applying an artificial dissipation that reduces the weight on non-local operators. We represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics to long times. We test this scheme by calculating spin and energy diffusion constants in a variety of physical models. By gradually weakening the dissipation, we are able to consistently extrapolate our results to the case of zero dissipation, thus estimating the physical diffusion constant with high precision.