Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver

摘要

We investigate the cluster size convergence of the energy and observables using two forms of densitymatrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated bythe dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- andtwo-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impuritysolver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is moreaccurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards thethermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and localmoment of the two-dimensional Hubbard model for U/t = 2,4,6. These results compare favorably with the bestdata available in the literature, and help resolve earlier uncertainties in the moment for U/t = 2.