# Erik van Loon

### Contact details

erik.van_loon AT teorfys.lu.se | |

Post | Division of Mathematical Physics |

### About me

I have been working as an Associate Senior University Lecturer at Lund University since March 2021. My main research interest is the study of strongly correlated electrons and their collective excitations. I am also involved in teaching at the bachelor and master/PhD level. More information about my teaching, research and publications can be found below.

Previously, I was working with Professor Wehling at the University of Bremen (2018-2021). I did my PhD with Professor Katsnelson at Radboud University (2013-2018). Radboud University is also where I studied Physics, with a research stay with Professor Alexander Lichtenstein in Hamburg for my MSc. thesis.

## MSc. and BSc. Thesis projects

Thesis projects on topics in condensed matter theory are available, with a focus on the quantum mechanics of correlated systems. Most projects will involve a combination of theoretical and computational studies. For MSc. thesis project, prior knowledge of advanced quantum mechanics and solid state physics are beneficial. If you are interested in doing a thesis project with me, please contact me via e-mail (see above) so that we can find a suitable project for you.

## Teaching

I am currently responsible for the courses FYSB23 and FYST25. More information about the courses can be found on their respective Canvas pages. Please contact me by e-mail if you encounter problems in the registration process or if you have questions about the course.

Basic Statistical Physics and Quantum Statistics (FYSB 23, next given Spring 2022)

Solid State Theory (FYST25/EXTP90/NAFY017, next given Spring 2022)

## Research

My main interest is the study of collective, many-particle excitations in strongly correlated electron systems. The Coulomb interaction between electrons leads to both spatial and temporal correlations between these particles. In strongly correlated systems, this effect is so strong that a description based on independent (quasi-)particles breaks down completely and alternative theoretical frameworks need to be found. Indeed, over the last three decades, it has emerged that temporal and spatial correlations can largely be separated and that the former can be captured in a mean-field fashion, the so-called Dynamical Mean-Field Theory. In this way, the correlation-driven Mott metal-insulator is found: sufficiently strong electronic repulsion can immobilize the electrons and make a system insulating, even when it should be a metal according to band theory.

My work has focused on the collective properties of this kind of systems: compressibility, magnetic susceptibility, dielectric function, charge-density waves, etc. Some of these can be studied within DMFT, but it turns out that spatial correlations are more important for these collective properties than they are for single-particle properties. Diagrammatic extensions of DMFT address this deficiency, by adding spatial correlations back onto the DMFT solution. An important aspect in these investigations is the issue of consistency: Approximate solutions can violate known exact properties of the system. We have shown that appropriate diagrammatic expansions recover several of the exact properties, including charge conservation and thermodynamic consistency of response functions.

Several diagrammatic extensions of DMFT exist, my work has focussed on two of them which are called the dual fermion and dual boson approach. During my PhD, I implemented the dual boson approach for single-orbital systems and used it to study plasmons and charge-density waves, among other things. I currently maintain an open source code for multi-orbital dual fermion calculations, which can be found here: github.com/egcpvanloon/dualfermion

## Publications

**Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited**

Erik G. C. P. van Loon

[arXiv:2110.11116]**Local Plaquette Physics as Key Ingredient of High-Temperature Superconductivity in Cuprates**M. Danilov, E.G.C.P. van Loon, S. Brener, S. Iskakov, M.I. Katsnelson, A.I. Lichtenstein

[arXiv:2107.11344]**Downfolding the Su-Schrieffer-Heeger model**

Arne Schobert, Jan Berges, Tim Wehling and Erik van Loon

SciPost Phys. 11, 079 (2021) [arXiv:2104.09207]**Random Phase Approximation for gapped systems: role of vertex corrections and applicability of the constrained random phase approximation**

Erik G. C. P. van Loon, Malte Rösner, Mikhail I. Katsnelson, Tim O. Wehling

Phys. Rev. B 104, 045134 (2021) [arXiv:2103.04419]**Downfolding approaches to electron-ion coupling: Constrained density-functional perturbation theory for molecules****A full gap above the Fermi level: the charge density wave of monolayer VS**_{2}**An efficient fluctuation exchange approach to low-temperature spin fluctuations and superconductivity: from the Hubbard model to Na**_{x}CoO_{2}⋅yH_{2}O**Second-order dual fermion for multi-orbital systems****The Bethe-Salpeter equation at the critical end-point of the Mott transition****Coulomb Engineering of two-dimensional Mott materials****Turbulent hydrodynamics in strongly correlated Kagome metals****Ab-initio phonon self-energies and fluctuation diagnostics of phonon anomalies: lattice instabilities from Dirac pseudospin physics in transition-metal dichalcogenides****Environmental control of charge density wave order in monolayer 2H-TaS**_{2}**Thermodynamics of the metal-insulator transition in the extended Hubbard model****Dual Boson approach with instantaneous interaction****Bandwidth renormalization due to the intersite Coulomb interaction****Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory****Fermion-boson vertex within Dynamical Mean-Field Theory****Second-order dual fermion approach to the Mott transition in the two-dimensional Hubbard model****Confining graphene plasmons to the ultimate limit****First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction****Precursors of the insulating state in the square-lattice Hubbard model****The extended Hubbard model with attractive interactions****Competing Coulomb and electron–phonon interactions in NbS**_{2}**Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory****A comparison between methods of analytical continuation for bosonic functions****From local to nonlocal correlations: The Dual Boson perspective****Capturing non-local interaction effects in the Hubbard model: optimal mappings and limits of applicability****Interaction-driven Lifshitz transition with dipolar fermions in optical lattices****Double occupancy in dynamical mean-field theory and the Dual Boson approach****Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems****Ultralong-range order in the Fermi-Hubbard model with long-range interactions****Thermodynamic consistency of the charge response in dynamical mean-field based approaches****Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model****Plasmons in Strongly Correlated Systems: Spectral Weight Transfer and Renormalized Dispersion****Collective charge excitations of strongly correlated electrons, vertex corrections, and gauge invariance**

### Popular Publications

**Faseovergangen door quantumonzekerheid**