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The GWΓ Method

Lecture Notes + Slides

• Lecture Slides
• Multi-Orbital and Non-collinear Spin Theory Notes

References

Schwinger Functional Derivative Technique

• Functional Derivative Technique
• Green's Function Formalism for Calculating Spin-Wave Spectra
• Functional approach to the electronic and bosonic dynamics of many-body systems perturbed with an arbitrary strong electron-boson interaction
• The Sources of Schwinger's Green's Functions
• THE GREENING OF QUANTUM FIELD THEORY GEORGE AND I
• Quantum Materials Theory, from Perturbation Theory to Dynamical-Mean Field Theory (lecture notes).

All Things GWΓ

• Hedin's Equations
• New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem
• Hedin's Equations for Superconductors
• Lars Hedin and the Quest for a Theory of Excited States
• Generalized Hedin's Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
• The GW Approximation
• Electronic Excitations: Density-Functional Versus Many-Body Green's-Function Approaches
• Beyond the quasiparticle approximation: Fully self-consistent GW calculations
• Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals
• All-Electron Self-Consistent GW Approximation: Application to Si, MnO, and NiO
• Quasiparticle Self-Consistent GW Theory
• First-principles treatment of Mott insulators: linearized QSGW+DMFT approach
• Hedin Equations, GW, GW+DMFT, and All That
• First Principles Approaches to Spectroscopic Properties of Complex Materials
• Benchmark of GW Approaches for the GW100 Test Set
• GW100: Benchmarking G0W0 for Molecular Systems
• Vertex Corrections
• Systematic Vertex Corrections through Iterative Solution of Hedin's Equations Beyond the GW Approximation
• Accurate Quasiparticle Spectra from Self-Consistent GW Calculations with Vertex Corrections
• Electronic structure of Na, K, Si, and LiF from self-consistent solution of Hedin's equations including vertex corrections
• Self-consistent solution of Hedin's equations: Semiconductors and insulators
• One-electron spectra and susceptibilities of the three-dimensional electron gas from self-consistent solutions of Hedin's equations
• Vertex corrections in self-consistent GWΓ calculations: ground state properties of vanadium
• Intermediate Coupling Model of the Cuprates
• Dynamical Vertex Approximation
• Toward a predictive theory of correlated materials
• T-Matrix
• Beyond the GW approximation: Combining correlation channels

Theoretical Spectroscopy

• Dynamic Structure Factor: An Introduction

Electron Pairing

• Superconducting pairing mediated by spin fluctuations from first principles
• Phenomenological theory of unconventional superconductivity
• Superconductivity from repulsive interaction
• Pairing in the two-dimensional Hubbard model from weak to strong coupling
• NEW MECHANISM FOR SUPERCONDUCTIVITY (Kohn and Luttinger)
• NEW MECHANISM FOR SUPERCONDUCTIVITY (Luttinger)

Electron-Phonon Coupling

• Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids
• Electron-phonon interactions from first principles
• First-principles approach to the electron-phonon interaction
• Density Functional Perturbation Theory and Electron Phonon Coupling (lecture notes)
• Electron-phonon interaction using Wannier functions

Non-Equilibrium Green's Functions

• Nonequilibrium Green's function approach to artificial atoms
• Solving the Two-time Kadanoff-Baym Equations: Application to Model Atoms and Molecules

Electronic Structure

• Database of Journal Articles and Book References on the Korringa-Kohn-Rostoker Green's Function Method
• VASP the GUIDE
• Using VASP at NERSC, NERSC User Training, Oakland, CA, June 5, 2015.
• Wannier90 User Guide
• Lecture notes from the WIEN2k-workshop 2016 at McMasters University, Hamilton (Canada)
• Munich SPRKKR band structure program

SPRGW Codes + Tutorials

• All levels of the code allow for multi-orbtial, spin-orbit coupling, and non-collinear magnetism
• Direct link to first-priciples derived Hamiltonians through wannier90
• ab initio eigenvalues and wave function projections can be imported from VASP through mProj
• Massively parallelized using ScaLAPACK and HDF5 with future plugins for GPU processing

Tutorials COMING SOON

Auxiliary Utilities: mProj
A post-processing utility for reading and utilizing eigenvalues and wave function projections from the Vienna Ab initio Simulation Package for use in beyond DFT calculations, obtaining electronic band structures and density of states in various basis including local rotations, and calculating various operator expectation values. Additionally, the site- and orbital-resolved excitonic eigenvectors and the excitonic wave function obtained from the Bethe-Salpeter equation can be calculated.

Tutorials COMING SOON

DFT: A Primer for Physical and Engineering Sciences

A series of four two-hour sessions, including hands-on examples
In today's ever-changing research landscape, robust and transferable methodologies are crucial to tackling new complex problems in correlated materials, catalysis, and molecular dynamics. DFT has proven to be a powerful framework, yielding insights in fundamental and applied research. This hands-on pilot workshop will focus on both the theoretical underpinnings of the DFT as well as its application to modern problems in physics, chemistry, biological and materials sciences, and engineering. Emphasis will be given to hands-on experiences in solving the Kohn-Sham equation using the pseudopotential projected augmented wave method as implemented in the Vienna ab initio simulation package (VASP). It is the aim of the workshop that the participants gain a broad understanding of what DFT based modeling can provide, and its fundamental limitations. We will also discuss how continuing development of ever more sophisticated density functionals is leading to the broadening of the reach of the DFT to new classes of materials.

This pilot course is aimed at both theoretical and experimental PhD students, postdocs and faculty to expose them to the fundamentals of the DFT framework and give them hands-on experience to leverage in their own research programs. The workshop will also be appropriate for senior level undergraduates and Masters students.

Course Materials

Lecture Slides

• Course Overview
• Lecture I: Highlights, Development, & Theoretical Basis of DFT
• Lecture II: Practical Implementation & Numerical Convergence
• Lecture III: Electronic Structure
• Lecture IV: Current Advances & Spectroscopies

Hands-on Slides

• Hands-on I: H₂ Bonding
• Hands-on II: Silicon and Allotropes of Iron
• Hands-on III: Adsorption Energy of Water on MoS₂ and Electronic Structure or multilayer MoS₂

Hands-on Tutorial Files

• Archive of Tutorials

       Note: The tutorial files were designed for the HPC center at Northeastern University and will not run out of the box on any system.

General Resources

• VASP Wiki
• DFT in a Nutshell
• Jacob's Ladder of Density Functional Approximations
• List of Quantum Chemistry and Solid-State Physics Codes

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