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

TL;DR

This study compares two density matrix embedding theory methods, CDMET and DCA-DMET, for the Hubbard model, demonstrating their convergence behaviors and providing accurate energy and moment estimates using a sign-problem free AFQMC solver.

Contribution

It introduces a dynamical cluster formulation of DMET and compares its convergence with the original, applying both to large impurity clusters in Hubbard models with AFQMC.

Findings

DCA-DMET converges faster to the thermodynamic limit.

Both methods produce accurate energy estimates for various U/t values.

Results help resolve previous uncertainties in local moments for U/t=2.

Abstract

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