Hydrodynamics of Lorentz symmetric systems: a quantum Monte Carlo study

We present a study on the hydrodynamic behavior of charge current in a Lorentz symmetric system: graphene at charge-neutrality. We compute the current profiles directly from Quantum Monte Carlo (QMC) simulations of the microscopic tight-binding model with long-range Coulomb interactions. This allows us to get results in a clean environment with all scattering channels being controlled by the parameters of the microscopic Hamiltonian and exact results delivered by QMC without further approximations. As a consequence, we can trace the emergence of continuous hy- drodynamics in the initially discrete lattice system. Special attention is paid to the emergence of macroscopic boundary conditions from microscopic details of the sample’s edges. Another important peculiarity is the decoupling of the charge current from the momentum flow in the Lorentz symmet- ric system, since the electrons and holes propagate in opposite directions with equal distribution functions. Using Boltzmann transport theory, we derive Navier-Stokes-type equations directly for the charge current, thus eliminating the need for any mechanism coupling the velocity field and charge current to explain the experimentally observed hydrodynamic flow profiles in graphene at half-filling. In this framework, the current diffusion coefficient replaces viscosity. QMC current profiles and the extracted temperature dependence for the current diffusion coefficient are in good agreement with the aforementioned theory, thus supporting our kinetic description of hydrodynamic currents in charge neutral graphene.