|Address:||Institut für Theoretische Physik|
|J.W. Goethe-Universität Frankfurt|
|60438 Frankfurt/Main, Germany|
|Phone:||+49 69 798 47830|
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.
I am currently working at Scientific Computing & Modelling in Amsterdam as PhD student in the European Industrial Doctorate program.
Phase diagram of the square lattice bilayer Hubbard model:
a variational Monte Carlo studyAbstract: 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]
Pattern formation in the dipolar Ising model on a two-dimensional honeycomb latticeAbstract: 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]
Variational Monte Carlo Method
for the Hubbard model
- The Variational Monte Carlo method
- The application of VMC to the Hubbard model
- hVMC - a free VMC code for the Hubbard model
- The bilayer Hubbard model
- Summary and conclusion
- Appendix: hVMC quick start guide
- Appendix: Parallelism in modern computers and the hVMC code
Institut für Theoretische Physik
J.W. Goethe-Universität Frankfurt
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.
und ihre Anwendung zur Simulation von Spinsystemen
- Grundlagen der Thermodynamik(Fundamentals of thermodynamics)
- Grundlagen der klassischen statistischen Physik(Fundamentals of classical statistical physics)
- Einführung in Monte Carlo Methoden(Introduction to Monte Carlo methods)
- Das eindimensionale Ising-Modell(The one-dimensional Ising model)
- Das zweidimensionale Ising-Modell(The two-dimensional Ising model)
- Ausblick: Ising-Modell mit Dipol-Dipol-Wechselwirkung(Outlook: The Ising model with dipole-dipole interaction)
- Zusammenfassung der Ergebnisse(Summary of the results)
Institut für Theoretische Physik
J.W. Goethe-Universität Frankfurt
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 strongly believe that the results of research done at public educational institutions should be made available to the general public free of charge. This also applies to software and I will therefore release everything that I write 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.
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
Implementation of the Variational Monte Carlo method for the Hubbard model
Deconvolution methods for analytic continuation
GPU architecture and its impact on GPGPU programming04.07.2012 - Student's talks as part of the high performance computing practical courseslides: gputalk.pdf
Pattern formation in the dipolar Ising model on a 2-dim. honeycomb lattice
The Heisenberg model and the Mermin-Wagner theorem: About the possibility of spontaneous symmetry breaking in low-dimensional systems25.01.2012 - Student's talks as part of the lecture: Introduction to solid state theoryslides: mwttalk.pdf
The Quantum Metropolis Algorithm: An implementation of Metropolis' famous algorithm on a quantum computer13.07.2011 - Student's talks as part of the lecture: Advanced solid state theoryslides: qmatalk.pdf
Monte Carlo methods in numerical integration
First steps with Linux[Prof. Eberhard Engel, April 2013]
Introduction to Astronomy I/II[Prof. René Reifarth, from summer term 2010 until summer term 2012]
Theoretical Physics 1+2: Classical mechanics[Prof. Marcus Bleicher, summer term 2011]