Bavarias, Germany

About Me


Hi, I'm a computational physicist and HPC advisor at PC², a national NHR-center for high-performance computing within the HPC.NRW competence network. As a freelancer, I also regulary give Julia workshops at undergraduate, graduate, and postgraduate level. Feel free to contact me if you're interested!

I obtained my PhD in the group of Prof. Simon Trebst at the University of Cologne in 2020. Previously, I studied and worked at the Goethe University, the University of Florida (Go Gators!) and the TU Darmstadt. I also had the pleasure of conducting longer research stays at Stanford University, the Weizmann Institute of Science, and the University of Chicago.

Julia Workshops

Julia is a beautiful young dynamic programming language created for numerical computing. It aims to be as intuitive as Python while still being as fast as statically compiled languages like Fortran and C. Julia is free to use, and all source code is publicly available on GitHub. Because of my passion for the language - it is my favorite programming language to use - I regularly teach Julia at undergraduate, graduate, and post-graduate level at the University of Cologne (check out our computer physics videos). I also give Julia workshops as a freelancer, most recently at the University of Oulu in Finland. Check out the repositories linked below to get an impression of some of the covered content. Somewhat related, I also gave a short talk at JuliaCon 2018 in London which you can find on youtube. You might also want to check out PhysicsTutorials.jl.

Latest/Upcoming Workshops


Metallic quantum criticality and high-temperature superconductivity

In this work, we present numerically exact results from sign-problem free quantum Monte Carlo simulations for a spin-fermion model near an \(O(3)\) symmetric antiferromagnetic (AFM) quantum critical point. We find a hierarchy of energy scales that emerges near the quantum critical point. At high energy scales, there is a broad regime characterized by Landau-damped order parameter dynamics with dynamical critical exponent \(z=2\), while the fermionic excitations remain coherent. The quantum critical magnetic fluctuations are well described by Hertz-Millis theory, except for a \(T^{-2}\) divergence of the static AFM susceptibility. This regime persists down to a lower energy scale, where the fermions become overdamped and concomitantly, a transition into a \(d-\)wave superconducting state occurs. These findings resemble earlier results for a spin-fermion model with easy-plane AFM fluctuations of an \(O(2)\) SDW order parameter, despite noticeable differences in the perturbative structure of the two theories. In the \(O(3)\) case, perturbative corrections to the spin-fermion vertex are expected to dominate at an additional energy scale, below which the \(z=2\) behavior breaks down, leading to a novel \(z=1\) fixed point with emergent local nesting at the hot spots [Schlief et. al. PRX 7, 2017]. Motivated by this prediction, we also consider a variant of the model where the hot spots are nearly locally nested. Within the available temperature range in our study (\(T\ge E_F/200\), we find substantial deviations from the \(z=2\) Hertz-Millis behavior, but no evidence for the predicted \(z=1\) criticality.

Reading: paper, talk, code, numerics paper, numerics package, thesis

Machine learning transport properties of quantum matter

Quantum many-fermion systems give rise to diverse states of matter that often reveal themselves in distinctive transport properties. While some of these states can be captured by microscopic models it remains challenging to numerically access their transport properties. Here we demonstrate that a machine learning technique dubbed quantum loop topography (QLT) can be used to directly probe transport by machine learning current-current correlations in imaginary time. We showcase this approach by studying the emergence of superconducting fluctuations in the negative-U Hubbard model and a spin-fermion model for a metallic quantum critical point. For both models, we find that the QLT approach detects a change in transport in very good agreement with their established phase diagrams. These proof-of-principle calculations combined with the numerical efficiency of the QLT approach point a way to identify hitherto elusive transport phenomena such as non-Fermi liquids using machine learning algorithms.

Reading: paper1, book article, paper2, thesis

Quasiparticle velocity renormalization in graphene

In this work, we take a systematic functional renormalization group (FRG) approach in studying graphene many-body effects at the Dirac point due to long-range Coulomb interactions. In particular, we examine the renormalization of the quasiparticle velocity, as observed in recent experiments, by establishing a low-energy effective QFT and deriving an infinite hierarchy of exact flow equations for the irreducible n-point vertices of the theory. By means of a scaling dimension analysis, we deduce a system of coupled integro-differential equations describing the momentum-dependent renormalized quasiparticle velocity and dielectric function in graphene at arbitrary scales. Focusing on the static screening limit, the full numerical solutions indicates that the linear low-energy dispersion (Dirac cone) gets strongly modified by long-range Coulomb interactions in the vicinity of the Dirac point.

Reading: paper, thesis, talk



"Identification of Non-Fermi Liquid Physics in a Quantum Critical Metal via Quantum Loop Topography"
George Driskell, Samuel Lederer, Carsten Bauer, Simon Trebst, and Eun-Ah Kim
Phys. Rev. Lett. 127, 046601
Cologne - Cornell


PhD thesis: "Simulating and machine learning quantum criticality in a nearly antiferromagnetic metal"
Advisor: Prof. Dr. Simon Trebst
Thesis PDF, Defense Talk

"Fast and stable determinant Quantum Monte Carlo"
Carsten Bauer
SciPost Phys. Core 2, 2 (source code @ GitHub)

"Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study"
Carsten Bauer, Yoni Schattner, Simon Trebst, and Erez Berg
Phys. Rev. Research 2, 023008 (source code @ GitHub)
Cologne - Stanford - Weizmann


"Machine Learning Transport Properties in Quantum Many-Fermion Simulations" (record entry)
Carsten Bauer, Simon Trebst
In NIC Symposium 2020, Vol. 50, pp. 85–92, Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag


"Probing transport in quantum many-fermion simulations via quantum loop topography"
Yi Zhang, Carsten Bauer, Peter Broecker, Simon Trebst, and Eun-Ah Kim
Phys. Rev. B 99, 161120(R), Editors' Suggestion
Cologne - Cornell


"Nonperturbative renormalization group calculation of quasiparticle velocity and dielectric function of graphene"
Carsten Bauer, Andreas Rückriegel, Anand Sharma, and Peter Kopietz
Phys. Rev. B 92, 121409(R)

Master's thesis: "Quasi-particle velocity renormalization in graphene"
Invited talk @ University of Cologne: "Quasi-particle velocity renormalization in graphene"
Advisor: Prof. Dr. Peter Kopietz


"Microwave-based tumor localization in moderate heterogeneous breast tissue"
Jochen Moll, Carsten Bauer, and Viktor Krozer
International Radar Symposium (Dresden, Germany), pp.877-884

All preprints on


Feel free to email me, even if it's just to say hello!



Paderborn Center for Parallel Computing | National HPC Center
Warburger Str. 100, 33098 Paderborn

Office: Cologne (remote work)
Phone: +49 5251-60-1716

Paderborn Center for Parallel Computing