ADG: automated generation and evaluation of many-body diagrams

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green’s function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0) of the code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.

A shortcut to the thermodynamic limit for quantum many-body calculations of metals

Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schrödinger equation are crucial for computational materials science. Methods such as coupled cluster theory show potential for widespread adoption if computational cost bottlenecks can be removed. For example, extremely dense k-point grids are required to model long-range electronic correlation effects, particularly for metals. Although these grids can be made more effective by averaging calculations over an offset (or twist angle), the resultant cost in time for coupled cluster theory is prohibitive. We show here that a single special twist angle can be found using the transition structure factor, which provides the same benefit as twist averaging with one or two orders of magnitude reduction in computational time. We demonstrate that this not only works for metal systems but also is applicable to a broader range of materials, including insulators and semiconductors.