Erik van Loon

dr. Erik G. C. P. van Loon
E-mail evloon at itp dot uni-bremen dot de
Room NW1 O3040
Otto-Hahn-Allee 1
University of Bremen
28359, Bremen, Germany
Telephone +49 421 218 62041

Since October 2018, I have been working in the group of prof. dr. Wehling at the University of Bremen. From December 2013 until September 2018, I was in the Theory of Condensed Matter group of prof. dr. Katsnelson, part of the Institute for Molecules and Materials of the Radboud University Nijmegen. On March 20 2018, I defended my PhD thesis Collective Phenomena in Strongly Correlated Systems. I finished my Master in the same group, having spent a year as an exchange student doing research in the group of prof. dr. Alexander Lichtenstein in Hamburg.

Research

I study the collective excitations in strongly correlated systems, especially in Hubbard-like models. Over the last two decades, Dynamical Mean-Field Theory (DMFT) has emerged as the best tool to describe the electronic structure of strongly correlated materials. It relies on mapping the full lattice problem with many degrees of freedom onto a self-consisent impurity problem. This impurity problem is simpler and can be solved (numerically) exactly using CT-QMC methods. It results in a local self-energy, which is then used for the lattice electrons. This approach has been hugely succesful at describing the Hubbard model, in particular the one-particle properties such as the density of states. DMFT can be used at arbitrary interaction strength, so the Mott transition from a weakly interacting metal to a strongly interacting insulator can be followed.

My work has focussed on the two-particles properties (e.g. the susceptibility and dielectric function) of the Hubbard model. These are rather difficult to determine computationally. The DMFT impurity problem gives some information about their local components. However, often we are also interested in the full momentum dependence. For example, the momentum dependence is necessary for determining the dispersion of collective modes such as plasmons, magnons and zero-sound modes. Many electrons at many different locations contribute to a collective mode, so the local description of DMFT is insufficient.

DMFT, with its good description of the local correlation, can be used as a starting point for a description of the momentum dependent susceptibility.
We are developing and implementing the dual boson approach, that incorporates nonlocal corrections to DMFT. An important aspect in these investigations is the issue of consistency: Approximate solutions can violate known exact properties of the system. For the case of the charge susceptibility, we have shown that the dual boson approach gives results satisfying the charge conservation law. This is in fact far from trivial and requires taking into account vertex corrections to all orders via the so-called ladder equation.
With this machinery, we have for the first time been able to study plasmons in the strongly correlated Hubbard model. In addition to this, we have used DMFT-based methods to investigate charge ordering in the extended Hubbard model, with applications to dipolar fermions in optical lattice, and the competition of electron-electron and electron-phonon interaction in NbS2.

Publications

  1. Dual Boson approach with instantaneous interaction
    L. Peters, E. G. C. P. van Loon, A. N. Rubtsov, A. I. Lichtenstein, M. I. Katsnelson, E. A. Stepanov
    [arXiv:1902.06604]
  2. Bandwidth renormalization due to the intersite Coulomb interaction
    Yann in ‘t Veld, Malte Schüler, Tim Wehling, Mikhail I. Katsnelson, Erik G. C. P. van Loon
    [arXiv:1901.11257]
  3. Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
    Friedrich Krien, Erik G. C. P. van Loon, Mikhail I. Katsnelson, Alexander I. Lichtenstein, Massimo Capone
    [arXiv:1811.00362]
  4. Fermion-boson vertex within Dynamical Mean-Field Theory
    Erik G. C. P. van Loon, Friedrich Krien, Hartmut Hafermann, Alexander I. Lichtenstein and Mikhail I. Katsnelson
    Phys. Rev. B 98, 205148 (2018)[arXiv:1806.10415]
  5. Second-order dual fermion approach to the Mott transition in the two-dimensional Hubbard model
    Erik G. C. P. van Loon, Mikhail I. Katsnelson and Hartmut Hafermann
    Phys. Rev. B 98, 155117 (2018)[arXiv:1805.08572]
  6. Confining graphene plasmons to the ultimate limit
    Alessandro Principi, Erik van Loon, Marco Polini and Mikhail I. Katsnelson
    Phys. Rev. B 98, 035427 (2018)[arXiv:1802.06797]
  7. First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction
    M. Schüler, E. G. C. P. van Loon, M. I. Katsnelson, T. O. Wehling
    Phys. Rev. B 97, 165135 (2018)[arXiv:1706.09644]
  8. Precursors of the insulating state in the square-lattice Hubbard model
    E. G. C. P. van Loon, Hartmut Hafermann and M. I. Katsnelson
    Phys. Rev. B 97, 085125 (2018)[arXiv:1712.08379]
  9. The extended Hubbard model with attractive interactions
    E. G. C. P. van Loon and M. I. Katsnelson
    J. Phys.: Conf. Ser., 1136, 012006 (2018)[arXiv:1709.06379]
  10. Competing Coulomb and electron–phonon interactions in NbS2
    E. G. C. P. van Loon, M. Rösner, G. Schönhoff, M. I. Katsnelson, T. O. Wehling
    npj Quantum Materials 3, 32 (2018)[arXiv:1707.05640]
  11. Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory
    F. Krien, E. G. C. P. van Loon, H. Hafermann, J. Otsuki, M. I. Katsnelson, A. I. Lichtenstein
    Phys. Rev. B 96, 075155 (2017)[arXiv:1706.10233]
  12. A comparison between methods of analytical continuation for bosonic functions
    Johan Schött, Erik G. C. P. van Loon, Inka L. M. Locht, Mikhail Katsnelson, Igor Di Marco
    Phys. Rev. B 94, 245140 (2016)[arXiv:1607.04212]
  13. From local to nonlocal correlations: The Dual Boson perspective
    E. A. Stepanov, A. Huber, E. G. C. P. van Loon, A. I. Lichtenstein, M. I. Katsnelson
    Phys. Rev. B 94, 205110 (2016)[arXiv:1604.07734]
  14. Capturing non-local interaction effects in the Hubbard model: optimal mappings and limits of applicability
    E. G. C. P. van Loon, M. Schüler, M. I. Katsnelson, T. O. Wehling
    Phys. Rev. B 94, 165141 (2016)[arXiv:1605.09140]
  15. Interaction-driven Lifshitz transition with dipolar fermions in optical lattices
    E. G. C. P. van Loon, M. I. Katsnelson, L. Chomaz, M. Lemeshko
    Phys. Rev. B 93, 195145 (2016)[arXiv:1603.09358]
  16. Double occupancy in dynamical mean-field theory and the Dual Boson approach
    Erik G. C. P. van Loon, Friedrich Krien, Hartmut Hafermann, Evgeny A. Stepanov, Alexander I. Lichtenstein, Mikhail I. Katsnelson
    Phys. Rev. B 93, 155162 (2016)[arXiv:1602.09129]
  17. Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems
    E. A. Stepanov, E. G. C. P. van Loon, A. A. Katanin, A. I. Lichtenstein, M. I. Katsnelson, A. N. Rubtsov
    Phys. Rev. B 93, 045107 (2016)[arXiv:1508.07237]
  18. Ultralong-range order in the Fermi-Hubbard model with long-range interactions
    Erik G. C. P. van Loon, Mikhail I. Katsnelson and Mikhail Lemeshko
    Phys. Rev. B 92, 081106(R) (2015)[arXiv:1506.06007]
  19. Thermodynamic consistency of the charge response in dynamical mean-field based approaches
    Erik G. C. P. van Loon, Hartmut Hafermann, Alexander I. Lichtenstein, and Mikhail I. Katsnelson
    Phys. Rev. B 92, 085106 (2015)[arXiv:1505.05305]
  20. Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
    Erik G. C. P. van Loon, Alexander I. Lichtenstein, Mikhail I. Katsnelson, Olivier Parcollet, and Hartmut Hafermann
    Phys. Rev. B 90, 235135 (2014)[arXiv:1408.2150]
  21. Plasmons in Strongly Correlated Systems: Spectral Weight Transfer and Renormalized Dispersion
    E. G. C. P. van Loon, H. Hafermann, A. I. Lichtenstein, A. N. Rubtsov, and M. I. Katsnelson
    Phys. Rev. Lett. 113, 246407 (2014)[arXiv:1406.6188]
  22. Collective charge excitations of strongly correlated electrons, vertex corrections, and gauge invariance
    Hartmut Hafermann, Erik G. C. P. van Loon, Mikhail I. Katsnelson, Alexander I. Lichtenstein, and Olivier Parcollet
    Phys. Rev. B 90, 235105 (2014)[arXiv:1406.6515]

Popular Publications

  1. Faseovergangen door quantumonzekerheid
    Jins de Jong, Lennert van Tilburg en Erik van Loon
    Nederland Tijdschrift voor Natuurkunde, november 2012