California, USA

I'm a postdoctoral theoretical physicist from Cologne, Germany, and a senior HPC consultant within the German National High-Performance Computing Alliance (NHR) at the Paderborn Center for Parallel Computing (PC2).

I obtained my PhD in the Computational Condensed Matter Physics group of Prof. Simon Trebst at the University of Cologne. Previously, I studied and worked at the Goethe University, the University of Florida (Go Gators!) and TU Darmstadt. Fortunately, I also had the distinct pleasure of conducting multi-month research stays at Stanford University, the University of Chicago, and the Weizmann Institute of Science.

I'm an active member of the Julia community and one of the JuliaCon co-organizers. I develop and maintain several Julia packages on GitHub (e.g. ThreadPinning.jl, LIKWID.jl, NUMA.jl, MonteCarlo.jl, ...).
As a freelancer, I give Julia workshops for graduate students and postdocs at public and private institutions. Feel free to contact me if you're interested!

I'm a founding member of the Project Incubator Committee at NumFOCUS.

Julia is a beautiful programming language for numerical computing that is free to use and open source. It explores the tradeoffs in language design for dynamic programming languages and aims to be as accessible as Python while still being as fast as statically compiled languages (eg. C, Fortran).

I regularly teach Julia, often with a focus on high-performance computing, at undergraduate, graduate, and post-graduate level at universities, research institutions, and companies. Go ahead and check out the repositories linked below to get an impression of some of the content and feel free to contact me if you're interested!

The next (public) workshop is "Julia for High-Performance Computing" and will be held in-person at the High-Performance Computing Center Stuttgart (HLRS).

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

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

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

A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory (RDMFT) formulation of the electronic structure problem. For that purpose, the density-matrix functional of the full system is decomposed into an indirectly coupled sum of density-matrix functionals for all its subsystems using the adaptive cluster approximation to RDMFT. The approximations involved in the decomposition and the adaptive cluster approximation itself can be systematically converged to the exact result. The solutions for the density-matrix functionals of the effective subsystems involves a constrained minimization over many-particle states that are approximated by parametrized trial states on the quantum computer similarly to the variational quantum eigensolver. The independence of the density-matrix functionals of the effective subsystems introduces a new level of parallelization and allows for the computational treatment of much larger molecules on a quantum computer with a given qubit count. In addition, for the proposed algorithm techniques are presented to reduce the qubit count, the number of quantum programs, as well as its depth. The new approach is demonstrated for Hubbard-like systems on IBM quantum computers based on superconducting transmon qubits.

Reading: paper, code

"Bridging HPC Communities through the Julia Programming Language"

Valentin Churavy, William F Godoy, **Carsten Bauer**, Hendrik Ranocha, Michael Schlottke-Lakemper, Ludovic Räss,

Johannes Blaschke, Mosè Giordano, Erik Schnetter, Samuel Omlin, Jeffrey S. Vetter, and Alan Edelman

arXiv:2211.02740

PC2 - MIT - ORNL - NERSC - HLRS - CSCS - and more

"Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers"

Robert Schade, **Carsten Bauer**, Konstantin Tamoev, Lukas Mazur, Christian Plessl, and Thomas D. Kühne

Phys. Rev. Research **4**, 033160

PC2 / NHR

"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)

Cologne

"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

Cologne

"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)

Frankfurt

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

Frankfurt

NHR @ PC²

Paderborn Center for Parallel Computing | National HPC Center

Warburger Str. 100, 33098 Paderborn

Office: Cologne (remote work)

Phone: +49 5251-60-1716

Email: carsten.bauer@upb.de