Reformulation of the nonlocal coherent-potential approximation as a unique reciprocal-space theory of disorder

Correlation effects in solids: From DFT to DMFT

“…We still should ¿nd an optimal way of periodization the CDMFT scheme. For the DCA approach one can average over different tiling of the Brillouine zone within the same cluster as was suggested for non-local CPA scheme [29]. For the CDMFT scheme the main problem is to ¿nd periodic self-energy solution, which preserve the analytical properties of the lattice Green's function [37].…”

“…In the free-cluster version of the CDMFT scheme [27] which is equivalent to the cellular DMFT method [28] or to the molecular CPA scheme in the alloy theory [29] we can make the following prescription. First, we need to integrate out the superlattice degrees of freedom, similar to the standard DMFT approach, and obtained the local Green's function matrix:…”

Generalized inclusion of short-range ordering effects in the coherent potential approximation for complex-unit-cell materials

“…21 Furthermore, this coarse-graining of the Brillouin zone leads to discontinuities in the k -dependent integrand of Eq.12, whenever tile boundaries are crossed. 24,26 We note here however a recent suggestion to overcome such limitation through an additional averaging step over various phase choices, to reobtain a smooth k -dependence 18 .…”

“…Jarrell et al, 20 and subsequently Rowlands et al, 21 have shown how this can be accomplished through a partitioning of the original Brillouin zone domain of integration respectful of the underlying lattice symmetries. This is now coarse-grained into N c tiles around a discrete set of cluster momenta K n , which remain defined only up to an arbitrary phase factor, further discussed below 24 .…”

“…14 Along the latter line of research, the non-local coherent potential approximation (NLCPA) has been recently developed based on insights provided by the Dynamical Cluster Approximation (DCA). 20 The method has shown its capability to describe SRO effects both within model Hamiltonian studies 18,[21][22][23][24] and when reimplemented within a completely self-consistent DFT-KKR framework for realistic systems. [25][26][27] This technique inherits however from its derivation a practical restriction to simple, one atom per unit cell lattices in Strukturberichte A h , A2 or A1 structures.…”