# 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. Prior to that, I was in the group of prof. dr. Wehling at the University of Bremen (2018-2021) and the Theory of Condensed Matter group at Radboud University Nijmegen (2013-2018), where I wrote my PhD thesis Collective Phenomena in Strongly Correlated Systems in the group of prof. dr. Katsnelson. Nijmegen is also where I studied Physics, with a research stay at the group of prof. dr. 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.

### 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.

My work has focused on the collective properties of this kind of systems: compressibility, magnetic susceptibility, dielectric function, charge-density waves, etc. Here, the spatial structure that was removed in DMFT becomes important again, since it determines the dispersion of collective modes (plasmons, magnons and zero-sound modes) as well as the precise character of charge-density waves. Briefly stated, the response of the full system is not the same as the response of the auxiliary mean-field model.

Diagrammatic extensions of DMFT address this deficiency, by adding spatial correlations back into 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.

I maintain an open source code for multi-orbital dual fermion calculations, which can be found here: github.com/egcpvanloon/dualfermion

My other research interests include downfolding of complicated electronic systems onto simpler low-energy models, for both electronic and lattice degrees of freedom.

## Publications

**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

[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

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