New method of computing correlation functions. I

W. Apel

Alexei A. Kananenka

Recent progress in materials synthesis combined with advances in computational science have opened up an opportunity to design new materials with specific properties. Semiconductors, heterostructures, and thin layered films are used for energy harvesting and solar cells. Transition metal oxides and metallic surfaces with deposited magnetic molecules are used for signal conversion, nonvolatile memory modules and spintronics. Due to growing complexity of the new materials the most efficient approach to their design requires combined experimental and theoretical effort. In order to advance our understanding of the complicated physics of the modern materials new theoretical methods based on controlled, reliable, computationally efficient and systematically improvable approximations describing correlation and finite-temperature effects are needed. Density functional theory (DFT) remains a method of choice for materials science calculations due to its low computational cost. However, despite all recent efforts, the majority DFT applications are limited to weakly correlated systems and zero temperature. The lack of systematic improvability, inaccurate treatment of strongly correlated systems will continue to restrict the domain of DFT applications. The multi-reference wave-function methods can provide an accurate description of the strongly correlated systems. Unfortunately, these methods are computationally expensive. In spite of recent improvement the computational complexity will likely to hinder the applications of wave-function based methods to materials science in foreseeable future. Finite-temperature Green's function methods offer several advantages such as systematic improvability, access to the excitation spectrum, thermodynamic properties and straightforward implementation of embedding frameworks. It has been realized long time ago and has been successfully used in condensed matter physics to study model systems. The applications of such methods to realistic systems are impeded due to lack of theoretical approaches providing chemical accuracy and efficient computational algorithms. In this dissertation, these shortcomings are addressed by developing self-energy embedding theory and its extensive comparison to established quantum chemistry methods. New numerical algorithms for efficient application of the finite-temperature Green's function methods to molecular and extended systems were developed. Properties of the second-order Green's function theory (GF2) in the context of quantum chemistry were investigated. Additionally, a new range-separated hybrid functional combining GF2 and DFT was developed and benchmarked.

Alexander L. Fetter

Andrea Dei, Lorenz Eberhardt

We exploit null vectors of the fractional Virasoro algebra of the symmetric product orbifold to compute correlation functions of twist fields in the large N limit. This yields a new method to derive correlation functions in these orbifold CFTs that is purely based on the symmetry algebra. We explore various generalisations, such as subleading (torus) contributions or correlation functions of other fields than the bare twist fields. We comment on the consequences of our computation for the AdS3/CFT2 correspondence.

Peter Schuck

J. E. Hirsch, J. R. Schrieffer

We propose a new algorithm to compute dynamic correlation functions in quantum systems at zero temperature using Monte Carlo techniques. The method, which avoids inverse-Laplace transforms, is based on a representation of the Dirac $\ensuremath{\delta}$ function as the limit of a Gaussian. We illustrate the method on the one-dimensional harmonic oscillator.