# EN AVDAT

Negev Desert, Israel

Hi, I'm a computational condensed matter physicist in the group of Prof. Dr. Simon Trebst at the University of Cologne. My research focuses on quantum phase transitions, where the interplay of thermal and quantum fluctuations gives rise to new exotic states of matter. In the vicinity of so-called metallic quantum critical points universal scaling laws emerge as a consequence of strong correlations. To gain a deeper understanding of these quantum critical effects, I develop and apply numerical tools such as Quantum Monte Carlo algorithms and (fancy) Machine Learning techniques, which allow for a comprehensive, unbiased study of relevant quantum field theories.

Apart from Cologne, 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.

## Science

#### 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, git repo, related paper

#### 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.

#### 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.

## Publications

### 2020

"Observation of non-Fermi liquid physics in a quantum critical region via quantum loop topography"
George Driskell, Samuel Lederer, Carsten Bauer, Simon Trebst, and Eun-Ah Kim
arXiv:2007.07898
Cologne - Cornell

"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

### 2019

"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

### 2018

"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

### 2015

"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"

### 2013

"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

## Contact

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

#### Office

Institut für Theoretische Physik
Universität zu Köln
Zülpicher Straße 77
50937 Köln

Office 2.05 Neubau TP
Phone: 0221-470-1053
Details: goo.gl/YxBVMz