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About me

I am a PhD student working in the European Union funded PROPAGATE project; a collaboration between the Amsterdam based software development company Scientific Computing & Modelling and the Free University of Amsterdam. So far, this means working as a software developer at SCM, where I am currently implementing time-dependent density functional based tight binding into the ADF molecular modeling suite.

Before that I was a master student in the condensed matter group of Prof. Valentí at the University of Frankfurt's Institute for Theoretical Physics, where I mostly worked with computational methods in condensed matter theory and statistical mechanics, especially Monte Carlo methods.


  • Robert Rüger, Erik van Lenthe, Thomas Heine, Lucas Visscher
    Tight-binding approximations to time-dependent density functional theory – A fast approach for the calculation of electronically excited states
    Abstract: We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB.
    published in: J. Chem. Phys. 144, 184103 (2016)
    eprint: arXiv:1603.02571 [physics.chem-ph]
  • Robert Rüger, Erik van Lenthe, You Lu, Johannes Frenzel, Thomas Heine, Lucas Visscher
    Efficient calculation of electronic absorption spectra by means of intensity-selected TD-DFTB
    Abstract: During the last two decades density functional based linear response approaches have become the de facto standard for the calculation of optical properties of small and medium-sized molecules. At the heart of these methods is the solution of an eigenvalue equation in the space of single-orbital transitions, whose quickly increasing number makes such calculations costly if not infeasible for larger molecules. This is especially true for time-dependent density functional tight binding (TD-DFTB), where the evaluation of the matrix elements is sufficiently cheap so that relatively large systems can be studied. We propose to do an oscillator strength based truncation of the single-orbital transition space to reduce the computational effort of TD-DFTB based absorption spectra calculations. We show that even a sizeable truncation does not destroy the principal features of the absorption spectrum, while naturally avoiding the unnecessary calculation of excitations with small oscillator strengths. We argue that the reduced computational cost of intensity-selected TD-DFTB together with its ease of use compared to other methods lowers the barrier of performing optical properties calculations of large molecules, and can serve to make such calculations possible in a wider array of applications.
    published in: J. Chem. Theory Comput., 2015, 11 (1), pp 157–167
    eprint: arXiv:1409.4521 [physics.chem-ph]
  • Robert Rüger, Luca F. Tocchio, Roser Valentí and Claudius Gros
    Phase diagram of the square lattice bilayer Hubbard model:
    a variational Monte Carlo study
    Abstract: We investigate the phase diagram of the square lattice bilayer Hubbard model at half filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of interlayer hopping t_perp and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: An antiferromagnetic Mott insulator at small t_perp for any value of U and a band insulator at large t_perp. At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t_perp a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a reentrant Mott insulator to metal transition and metal to band insulator transition for increasing t_perp in the range of 5.5t < U < 7.5t. Finally, we discuss the obtained phase diagrams in relation to previous studies based on different many-body approaches.
    published in: New J. Phys. 16 (2014) 033010
    eprint: arXiv:1311.6504 [cond-mat.str-el]
  • Robert Rüger and Roser Valentí
    Pattern formation in the dipolar Ising model on a two-dimensional honeycomb lattice
    Abstract: We present Monte Carlo simulation results for a two-dimensional Ising model with ferromagnetic nearest-neighbor couplings and a competing long-range dipolar interaction on a honeycomb lattice. Both structural and thermodynamic properties are very similar to the case of a square lattice, with the exception that structures reflect the sixfold rotational symmetry of the underlying honeycomb lattice. To deal with the long-range nature of the dipolar interaction we also present a simple method of evaluating effective interaction coefficients, which can be regarded as a more straightforward alternative to the prevalent Ewald summation techniques.
    published in: Phys. Rev. B 86, 024431 (2012)
    eprint: arXiv:1207.1864 [cond-mat.stat-mech]

M.Sc. Thesis

Implementation of the
Variational Monte Carlo Method
for the Hubbard model
  1. Introduction
  2. The Variational Monte Carlo method
  3. The application of VMC to the Hubbard model
  4. hVMC - a free VMC code for the Hubbard model
  5. The bilayer Hubbard model
  6. Summary and conclusion
  7. Appendix: hVMC quick start guide
  8. Appendix: Parallelism in modern computers and the hVMC code
Advisor: Prof. Valentí
Institut für Theoretische Physik
J.W. Goethe-Universität Frankfurt
August 2013

The full text of the thesis can be downloaded here.

I've released the Variational Monte Carlo code for the Hubbard model that I wrote as a part of this thesis as free software. See below for a brief description and instructions on where to get the code.

B.Sc. Thesis

Monte Carlo Methoden in der statistischen Physik
und ihre Anwendung zur Simulation von Spinsystemen
(Monte Carlo methods in statistical physics and their application to the simulation of spin systems)
  1. Einleitung
  2. Grundlagen der Thermodynamik
    (Fundamentals of thermodynamics)
  3. Grundlagen der klassischen statistischen Physik
    (Fundamentals of classical statistical physics)
  4. Einführung in Monte Carlo Methoden
    (Introduction to Monte Carlo methods)
  5. Das eindimensionale Ising-Modell
    (The one-dimensional Ising model)
  6. Das zweidimensionale Ising-Modell
    (The two-dimensional Ising model)
  7. Ausblick: Ising-Modell mit Dipol-Dipol-Wechselwirkung
    (Outlook: The Ising model with dipole-dipole interaction)
  8. Zusammenfassung der Ergebnisse
    (Summary of the results)
Advisor: Prof. Valentí
Institut für Theoretische Physik
J.W. Goethe-Universität Frankfurt
September 2011

My thesis is available in full text and as LaTeX source code. Feel free to use the source code as a template for your own thesis!

I've released the source code of the simulation software SSMC that I wrote as a part of this thesis. See below for a brief description and instructions on where to get the code. Note that the code in my thesis' appendix is an old and outdated version of the released.


I believe that the results of research done at public educational institutions should be freely available to the general public. This also applies to software and I have therefore released everything that I wrote during my studies as free and open source software under the GPLv3+ license. You can get the source codes on my GitHub page. Feel free to write me an email with any problems (or bugs!) that you run into!

  • hVMC is a free Variational Monte Carlo code for the Hubbard model that I have written as a part of my master's thesis. Read my master's thesis if you want to know how the code works or how to use it! On the right you see the double occupation density of the bilayer Hubbard model as a function of the interplane hopping. The step in the light blue curve is quite interesting as it show a metallic phase in between two insulating phases. Read the article if you want to know more!

  • SSMC is a Monte Carlo simulation code for classical spin systems like the Ising model that I originally started to write as a part of my bachlor's thesis. It has grown quite a bit since then and by now has some rather advanced features like the simulation of spin systems with dipolar interactions or cluster updates. Check out the README that comes with SSMC! It should give you a head start in using, understanding and modifying SSMC.

  • MFHUB is a very small and simple code that performs mean field calculations for the two dimensional Hubbard model on a triangular lattice. It was written as an exercise for the computational methods in solid state theory lecture. In order to understand what MFHUB does, I suggest that you take a look at the corresponding lecture notes and the exercise that MFHUB attempts to solve. There is a README that explains how to use MFHUB.

  • RC4 is a simple Python2 implementation of the popular game "Connect Four"! I played around a little bit with writing an AI that actually deserves this name and the result is not as dumb as one might think, considering that I have no expertise in this field whatsoever! Try it! I think it's pretty difficult to win against it, but I might just be horribly bad at the game ;-) ...

    The picture on the right is a screenshot of a game I had against the AI. The AI is player two and actually managed to get me into a triple bind!

Talks & Posters


  • First steps with Linux
    [Prof. Eberhard Engel, Goethe University Frankfurt, April 2013]
  • Introduction to Astronomy I/II
    [Prof. René Reifarth, Goethe Univ. Frankfurt, summer term 2010 - summer term 2012]
  • Theoretical Physics 1+2: Classical mechanics
    [Prof. Marcus Bleicher, Goethe University Frankfurt, summer term 2011]