Hydrodynamics of Lorentz symmetric systems: a quantum Monte Carlo study

Abstract: 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. Other: MU (AR) thanks the DFG for financial support un- der the projects UL444/2-1, Project number 495044360 (AS120/19-1, Project number 530989922). FFA ac- knowledges financial support from the DFG through the W¨urzburg-Dresden Cluster of Excellence on Complex- ity and Topology in Quantum Matter - ct.qmat (EXC 2147, Project No. 390858490) as well as the SFB 1170 on Topological and Correlated Electronics at Surfaces and Interfaces (Project No. 258499086). KP acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG) via the Emmy Noether Programme (Quantum Design grant, ME4844/1, project- id 327807255), project A04 of the Collaborative Research Center SFB 1143 (project- id 247310070), and the Cluster of Excellence on Com- plexity and Topology in Quantum Matter ct.qmat (EXC 2147, project-id 390858490). We gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss- centre.eu) for funding this project by providing com- puting time for the computation of the current-current correlator on the GCS Supercomputer SUPERMUC- NG at the Leibniz Supercomputing Centre (www.lrz.de, project number pn73xu), as well as the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg (FAU) under the NHR project b133ae to carry out the SAC analysis. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is par- tially funded by the German Research Foundation (DFG) – 440719683. JUWELS supercomputer was used for the calculation of E tensor. The numerical calcula- tions were carried out with the Algorithms for Lattice Fermions (ALF) library.