Correlated quantum dynamics of graphene

TL;DR

This paper evaluates the fermionic Truncated Wigner Approximation (fTWA) for simulating the dynamics of graphene-like systems within the Fermi-Hubbard model, demonstrating improved accuracy over mean-field methods and good agreement with exact solutions.

Contribution

It introduces and assesses the fTWA method for modeling correlated quantum dynamics in graphene-like systems, showing its efficiency and accuracy.

Findings

fTWA captures site occupation and correlation dynamics better than Hartree-Fock.

Good agreement between fTWA and exact diagonalization for small systems.

fTWA scales similarly to Hartree-Fock, enabling larger system simulations.

Abstract

Phase-space representations are a family of methods for dynamics of both bosonic and fermionic systems, that work by mapping the system's density matrix to a quasi-probability density and the Liouville-von Neumann equation of the Hamiltonian to a corresponding density differential equation for the probability. We investigate here the accuracy and the computational efficiency of one approximate phase-space representation, called the fermionic Truncated Wigner Approximation (fTWA), applied to the Fermi-Hubbard model. On a many-body 2D system, with hopping strength and Coulomb $U$ tuned to represent the electronic structure of graphene, the method is found to be able to capture the time evolution of first-order (site occupation) and second-order (correlation functions) moments significantly better than the mean-field, Hartree-Fock method. The fTWA was also compared to results from the exact diagonalization method for smaller systems, and in general the agreement was found to be good. The fully parallel computational requirement of fTWA scales in the same order as the Hartree-Fock method, and the largest system considered here contained 198 lattice sites.