Extra condition is necessary to have a unique cluster wave vectors set in the periodic cluster approximations

Abstract

We added an extra condition, original lattice symmetry of chosen cluster around cluster central site, to the cluster approximation methods with periodic boundary condition such as dynamical cluster approximation (DCA), effective medium approximation (EMSCA) and nonlocal coherent potential approximation (NLCPA). For each cluster size, this condition leads to a unique cluster wave vectors set in the first Brillouin zone (FBZ) where they preserve full symmetry of first Brillouin zone around ${\bf K=0}$. In this case whole cluster wave vectors are restricted to the FBZ and when number of sites in the cluster is equal to the whole lattice sites, these approximations recover original lattice symmetry in real and k-spaces.