Dissipation-assisted operator evolution method for capturing hydrodynamic transport

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 acting on long 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 follow 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.

Automated summary

We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. By applying an artificial dissipation to long operators, we are able to track the dynamics to long times and estimate the physical diffusion constant with high precision.