Cluster-size dependence in cellular dynamical mean-field theory

TL;DR

This study investigates how the size of clusters affects cellular dynamical mean-field theory results for the 2D Hubbard model, finding that cumulant periodization accelerates convergence and small clusters can capture essential physics.

Contribution

It demonstrates that cumulant periodization improves convergence in CDMFT and shows small clusters can effectively represent doped Mott insulator physics.

Findings

Cumulant periodization yields fastest convergence.

Convergence is faster near (0,0) and (pi/2,pi/2).

4-site results agree well with 16-site results.

Abstract

We examine the cluster-size dependence of the cellular dynamical mean-field theory (CDMFT) applied to the two-dimensional Hubbard model. Employing the continuous-time quantum Monte Carlo method as the solver for the effective cluster model, we obtain CDMFT solutions for 4-, 8-, 12-, and 16-site clusters at a low temperature. Comparing various periodization schemes, which are used to construct the infinite-lattice quantities from the cluster results, we find that the cumulant periodization yields the fastest convergence for the hole-doped Mott insulator where the most severe size dependence is expected. We also find that the convergence is much faster around (0,0) and (pi/2,pi/2) than around (pi,0) and (pi,pi). The cumulant-periodized self-energy seems to be close to its thermodynamic limit already for a 16-site cluster in the range of parameters studied. The 4-site results remarkably agree well with the 16-site results, indicating that the previous studies based on the 4-site cluster capture the essence of the physics of doped Mott insulators.