Two Quantum Cluster Approximations
Abstract
We provide microscopic diagrammatic derivations of the Molecular Coherent Potential Approximation (MCA) and Dynamical Cluster Approximation (DCA) and show that both are Phi-derivable. The MCA (DCA) maps the lattice onto a self-consistently embedded cluster with open (periodic) boundary conditions, and therefore violates (preserves) the translational symmetry of the original lattice. As a consequence of the boundary conditions, the MCA (DCA) converges slowly (quickly) with corrections O(1/Lc) (O(1/Lc^2)), where Lc is the linear size of the cluster. However, local quantities, when measured in the center of the MCA cluster, converge more quickly than the DCA result. These results are demonstrated numerically for the one-dimensional symmetric Falicov-Kimball model.
Cite
@article{arxiv.cond-mat/0205460,
title = {Two Quantum Cluster Approximations},
author = {Th. A. Maier and O. Gonzalez and M. Jarrell and Th. Schulthess},
journal= {arXiv preprint arXiv:cond-mat/0205460},
year = {2007}
}
Comments
16 pages, 6 figures; to be published in proceedings of the XV Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics (Springer Proceedings in Physics)