New Algebraic Formulation of Density Functional Calculation

This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to the derivation and transcription of a few lines of algebra. This new framework enables us to concisely demystify the inner workings of fully functional, highly efficient modern ab initio codes and to give complete instructions for the construction of such for calculations employing arbitrary basis sets. Within this framework, we also discuss in full detail a variety of leading-edge ab initio techniques, minimization algorithms, and highly efficient computational kernels for use with scalar as well as shared and distributed-memory supercomputer architectures

Bond-dependent slave-particle cluster theory based on density matrix expansion

We introduce a cluster slave-particle theory for Hubbard models based on a density matrix expansion approach over overlapping real-space clusters. We improve on prior slave-particle approaches by extending the description of the slave operators to correctly describe particle hopping along bonds between sites in the system. The interacting lattice slave-particle problem is then turned into a set of overlapping real-space clusters which are solved self-consistently and with appropriate physical matching constraints at shared lattice sites between clusters. Our cluster expansion approach leads to an exact description for short-ranged correlations with the cluster radius and joins that smoothly to an approximated description of long-ranged correlations. Specifically, it avoids making large errors caused by cutting bonds at cluster boundaries. We test our theory in 1D and 2D $d$-$p$ Hubbard model and compare it to exact ground-state benchmark results. Our method produces accurate total energies, site occupancies, and double occupancies with modest computational costs.Comment: 19 pages, 12 figure