Continuous momentum dependence in the dynamical cluster approximation
Abstract
The dynamical cluster approximation (DCA) is a quantum cluster extension to the single-site dynamical mean-field theory that incorporates spatially nonlocal dynamic correlations systematically and nonperturbatively. The DCA algorithm addresses the cluster shape dependence of the DCA and improves the convergence with cluster size by introducing a lattice self-energy with continuous momentum dependence. However, we show that the DCA algorithm is plagued by a fundamental problem when its self-consistency equations are formulated using the bare Green's function of the cluster. This problem is most severe in the strongly correlated regime at low doping, where the DCA self-energy becomes overly metallic and local, and persists to cluster sizes where the standard DCA has long converged. In view of the failure of the DCA algorithm, we propose to complement DCA simulations with a post-interpolation procedure for single-particle and two-particle correlation functions to preserve continuous momentum dependence and the associated benefits in the DCA. We demonstrate the effectiveness of this practical approach with results for the half-filled and hole-doped two-dimensional Hubbard model.
Keywords
Cite
@article{arxiv.2002.06866,
title = {Continuous momentum dependence in the dynamical cluster approximation},
author = {Urs R. Hähner and Thomas A. Maier and Thomas C. Schulthess},
journal= {arXiv preprint arXiv:2002.06866},
year = {2020}
}
Comments
11 pages, 10 figures