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We investigate the cluster size convergence of the energy and observablesusing two forms of density matrix embedding theory (DMET): the original clusterform (CDMET) and a new formulation motivated by the dynamical clusterapproximation (DCA-DMET). Both methods are applied to the half-filled one- andtwo-dimensional Hubbard models using a sign-problem free auxiliary-fieldquantum Monte Carlo (AFQMC) impurity solver, which allows for the treatment oflarge impurity clusters of up to 100 sites. While CDMET is more accurate atsmaller impurity cluster sizes, DCA- DMET exhibits faster asymptoticconvergence towards the thermodynamic limit (TDL). We use our two formulationsto produce new accurate estimates for the energy and local moment of thetwo-dimensional Hubbard model for U/t = 2, 4, 6. These results comparefavourably with the best data available in literature, and help resolve earlieruncertainties in the moment for U/t = 2.

physical review. b./physical review. b

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