# Informal Friday Talks

### Friday 30 April 2021, 2pm

Gabriel Topp (Aalto University) and Christian Eckhardt (RWTH Aachen + MPSD Hamburg): Light-matter coupling and quantum geometry in moiré materials

The experimental tunability of moiré materials makes them a promising candidate for the potential integration into future optoelectronic devices. The versatile quantum phase diagram of these twisted heterostructures is determined by the emergence of flat electronic bands. From a classical, single-band point of view, the diverging effective mass of an electron moving within a flat band demands a vanishing light-matter interaction. However, recent theoretical [1] and experimental efforts [2] find significant light-matter couplings to the flat electronic bands in twisted bilayer graphene. By investigating light-matter couplings in a generic multi-band Hamiltonian, we point out quantum geometric contributions to the light-matter coupling that depend on the electronic wave function. Employing an educative 1D model, we prove that these nontrivial multi-band contributions yield finite couplings even for entirely flat electronic bands. Finally, we utilise these fundamental insights to investigate static light-matter couplings and the dynamical Floquet response of magic-angle twisted bilayer graphene in a realistic tight-binding model [3].

[1] G. E. Topp, G. Jotzu, J. W. McIver, L. Xian, A. Rubio, and M. A. Sentef “Topological Floquet engineering of twisted bilayer graphene”, Phys. Rev. Research 1, 023031 (2019)

[2] B. Deng, C. Ma, Q. Wang, S. Yuan, K. Watanabe,T. Taniguchi, F. Zhang, and F. Xia "Strong mid-infrared photoresponse in small-twist-angle bilayer graphene", Nature Photonics 14, 49–553 (2020)

[3] G. E. Topp, C. J. Eckhardt, D. M. Kennes, M. A. Sentef, and P. Törmä “Light-matter coupling and quantum geometry in moiré materials”, arXiv:2103.04967 (03/2021)

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### Friday 09 April 2021, 2pm

Kirsten Fischer: A Statistical View on Deep Networks: Decomposition of Network Mappings and Training on Data Statistics

Understanding the functional principles of information processing in deep neural networks continues to be a challenge, in particular for networks with trained and thus non-random weights. To address this issue, we describe the mapping implemented by a deep network as a mapping between probability distributions. We characterize this mapping as an iterated transformation of Gaussian distributions where the non-linearity in each layer mixes mean and covariance. This allows us to identify different information coding paradigms corresponding to different local minima in the loss landscape, and moreover to selectively train networks on data statistics as opposed to data samples. Applied to an XOR task and to MNIST, we find that the mean and covariance of each class already encode class membership and provide sufficient information to solve these tasks. This analysis provides a quantitative and explainable perspective on classification.

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### Friday 12 February 2021, 2pm

Sebastian Miles: Universal properties of the boundary charge in 1D continuous systems

The connection between the quantum Hall effect (QHE) to periodically modulated nanowires allows to relate the physical QHE currents to fractional boundary charges in 1D systems. A study of the boundary charge for 1D continuous systems has revealed a set of interesting universal properties with respect to variation of the periodic modulation. The significance of the gauge choice for the study of boundary phenomena is emphasized and a construction is presented that implements the suggested gauge from first principles. The relation of the boundary charge to topological winding numbers is demonstrated and a universal linear dependence of the boundary charge on the periodic modulation is confirmed. The impact and occurrence of touching points is discussed and related to fundamental aspects of the band eigenstates as well as the band Chern number. Numerical studies will be presented to illustrate the findings.

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### Friday 15 January 2021, 2pm

Yuchi He: A basic introduction to one-dimensional topological phases

In this presentation, I will give a basic introduction to one-dimensional topological phases.

These phases are formally known as symmetry protected topological (SPT) phases. I will explain

how they are different from Landau-Ginzburg phases such as ferromagnetism, and topologically

ordered phases such as Laughlin states. I will also explain the basic idea of using "symmetry

fractionalization" to classify gapped SPT phases. Finally, I will mention some research progress

towards generalizations to higher dimensions as well as gapless systems.

### Friday 11 December 2020, 2pm

Tanay Nag: Anomalous and normal dislocation modes in Floquet topological insulators

Electronic band structure featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For example, a suitable periodic drive can convert a trivial state into a Floquet topological one, accommodating nondissipative dynamic gapless modes at the interfaces with vacuum. Here we theoretically demonstrate that dislocations, ubiquitous lattice defects in crystals, can probe Floquet topological and an unconventional $\pi$-trivial insulators in the bulk of a driven quantum system by supporting normal and anomalous modes at its core. Respectively they reside at the Floquet zone center and boundary. We exemplify these outcomes specifically for two-dimensional Floquet Chern insulator and $p_x+i p_y$ superconductor, where these localized modes are respectively constituted by charged and neutral Majorana fermions. Our findings should be instrumental in probing Floquet topological phases in the state-of-the-art experiments in driven quantum crystals and metamaterials through bulk topological lattice defects.

### Friday 04 December 2020, 2pm

Giacomo Passetti: Out Of Equilibrium Dynamics of a Quantum System

What happens when a quantum system is brought out of equilibrium and left free to evolve in time?

I will introduce the simple idea of a Quantum Quench, which is a protocol used to bring a quantum

system out of equilibrium. We are going to see how the unitary nature of time evolution seems to

prevent isolated systems to reach a “traditional” thermal state and how this has been tried to be

understood in terms of the Eigenstate Thermalization Hypothesis. Other than the asymptotic

behaviour, it is also interesting to look at what happens in the transient regime and see how

an inherent quantum critical point can reserve some “surprise” when we study the dynamical

evolution.

After having defined the framework, in this talk I will present my master study of the quench of a

particular 1D system, a wire of non interacting fermions with a spin orbit coupling and an external

magnetic field, trying to highlight the main physical contents of the final results.

### Friday 13 November 2020, 2pm

Martin Maurer: Flavortronics: Understanding coherences and negative differential conductance in quantum-dot transport in everyday physics terms

The discreteness of energy levels in quantum dots causes a variety of remarkable effects in the electronic transport. Among these effects is the typical current staircase that arises when a bias voltage across the dot is applied. This staircase is strongly modified when coherent superpositions of dot states may form. One remarkable consequence is the appearance of regions of negative differential conductance, where the current decreases with increasing bias voltage.

I will begin my talk by introducing quantum-dot-transport basics and explaining how the current staircase arises. The main topic will be the Flavortronics framework for strongly interacting multilevel quantum dots that are weakly coupled to metallic reservoirs. In particular, I will present kinetic equations that allow us to understand the dot dynamics and negative differential conductance in terms of intuitive processes: accumulation, relaxation, and rotation of a vector that describes the dot state.

### Friday 29 May 2020, 2pm

Kiryl Piasotski: Rational quantization of the boundary charge and universal properties of its fluctuations: a low-energy description

In my talk, I'm going to discuss the universal properties of a rather intriguing physical quantity, the charge hosted by a boundary of a generic one-dimensional insulator with a single orbital per site and nearest-neighbor hopping. First I'm going to show that in the vicinity of an arbitrary energetic band gap, all 1D insulators of the above-mentioned type admit for a universal description in terms of a one-dimensional Dirac-like Hamiltonian with a composite gap mechanism and, as we are going to see, one may relate the effective gap parameters of the low energy Hamiltonian to the microscopic ones in a deterministic fashion by means of Brillouin-Wigner perturbation theory. With the help of the low-energy model, one may then elegantly analyze the properties of the boundary charge, in particular, I will demonstrate that by appropriately tuning the model parameters one can achieve arbitrary rational charges (electron charge) times p/q with p and q being natural number-valued. As we are also going to see, the previous studies of fractional charges hosted by the interfaces generated by the coupling of fermions to the bose fields with broken discrete symmetry (solitons), may be easily incorporated into our picture and are nothing but the sum of the boundary charges right and left to the interface. Further, we are going to analyze the effects of strong short-range Coulomb interactions on the boundary and interface charge quantization by means of bosonization and perturbative renormalization group analysis. Finally, I'm going to discuss our recent developments related to the sharpness of the boundary charge as a quantum observable. As I'm going to show, to the leading order in 1/(the scale on which the charge probe smoothly looses) the fluctuations of the boundary charge show a critical 1/(energy gap) behaviour signifying the topological quantum phase transition at a gap-closing point. In the presence of the electron-electron scattering, we are going to see that one obtains a critical power-law 1/(gap to the power x), where x is an interaction strength dependent constant.

### Friday 15 May 2020, 2pm

Jonas Hauck.: Real-space Functional Renormalization Group - Application to Penrose Crystals

Quasi crystals are systems which have a long range order but no translational symmetry. These two properties make those systems on the one hand difficult to investigate numerically, as most of the standard methods rely on the translational invariance of the systems to get an efficient treatment, but on the other hand very interesting, as there exist states between Anderson localization and free states as well as fractional ordered states. One of the most well known examples is the five-fold rotationally symmetric Penrose lattice. We here expand the real-space FRG, recently developed for 1D Systems, to 2D by linking it to the Truncated Unity FRG approach. This new method is then applied to three different variations of the Penrose Model. The method we employ is capable of incorporating competing order instabilities on an equal footage and therefore examining the competition between Charge-Density wave and Spin-Density wave phases upon applying long range interactions. The analysis suggest that those phases can coexist in spatially separated parts of the lattice.

### Thursday 09 April, 2020, 2pm

Lukas Weber: Stochastic Series Expansion Quantum Monte Carlo

It is important to know how to flip your spins in a way that obeys detailed balance to efficiently simulate quantum magnets. A powerful, unbiased approach is the so-called Stochastic Series Expansion which we will discuss along with some more general aspects of Quantum Monte Carlo such as the infamous “sign problem”.

### Friday 14 February 2020, 2pm

Lennart Klebl: Ordering in Twisted Graphene Bilayers

Twisted bilayer graphene has become a very vivid field of research both theoretically and experimentally since superconductivity was found in an experiment in 2018. The band structure is highly controllable by experimental parameters which in theory makes this material an ideal testbed for the study of electronic correlations. In certain 'magic' twist angles, the bands closest to charge neutrality are very flat and should thus enhance interaction effects. The flat bands lead to several distinct magnetic ordering tendencies found in both an RPA study and FRG. The nature of superconductivity remains an open question we might be able to address in future works.

### Friday 07 February 2020, 2pm

Jannis Ehrlich: Catch the error

Most of the time in theoretical physics you develop your code. While writing code, however, there will occur errors which may give rise to unphysical behavior. To avoid this, your code has to be thoroughly tested if the results are correct. Even more important, the results should not change when the code is refactored to increase speed or new

features are implemented. As errors occur rather on the low level of simple routines, it is useful to test them separately, without comparing files manually. You can delegate this work to testing frameworks - which can be run by a simple command and tell you about errors.

In my talk I will present some ideas about tests, test- or behavioral driven development, and show the usage of a testing framework based on Catch2 (C++). If you want to find a testing framework for your favored programming language you may have a look at the corresponding Wikipedia page https://en.wikipedia.org/wiki/List_of_unit_testing_frameworks

### Friday 24 January 2020, 3pm

Jacob Beyer: Using the ubiquitous and very useful version control system git

Would you like to talk about Git, our lord and saviour?

Yes? Well you are in luck. This talk will exclusively focus on version control using git. Some basic instructions and commands will be presented in the start, but some - in my experience - useful tips and tricks will form the core of the talk.

### Friday, 15 February 2019, 2.30pm (26C 401)

Konstantin Nestmann:

How general are time-local master equations?

I will explore which evolutions of open quantum systems can be described using time-local master equations, specifically their relation to markovian dynamics and the question if genuinely non-markovian situations can be described using a time-local formalism.

### Friday, 1 February 2019, 2.30pm (MBP2 116)

Feng Xiong:

Topological semimetals

Topological materials and their correspondent exotic physical properties have been explored widely not only in theory but also in experiments. This talk I want to share the main history of the discovery of topological family including topological insulator, semimetal and recently nodal line semimetals. By using symmetry classification, people can denote different system with certain topological invariant number. Most importantly, there is a close correspondence between bulk and surface states. At last, I also like to share model’s construction about nodal line semimetal to form various topologies in 3d BZ and discuss about what we can further explore in this field.

### Friday, 18 January 2019, 2.30pm (MBP2 116)

Niclas Müller:

Topology in Floquet systems

Topological phases of matter have gained much interest in the last decade. These are systems whose electronic properties are dictated by the geometry of the (gapped) bandstructure. A topologically nontrivial bandstructure has no measurable consequences in the bulk of the system but leads to topologically protected exponentially localized edge states (TES) lying inside the bulk gap of a finite sample. Due to their unique properties the TES's are promising candidates for the realization of qubits in solid state systems.

### Friday, 30 November 2018, 2.30pm (26C/401)

Yen-Ting Lin:

Topology and Majorana fermions in quantum wires

A review of A. Yu Kitaev Uspekhi Fizicheskikh Nauk . **44 **131 (2001)

### Friday, 9 November 2018, 2.30pm (26C/401)

Viktor Reimer:

What Kraus operators can tell us about open-system dynamics

I will talk about general open-system dynamics and in particularly focus on the Kraus operator-sum representation. Its general properties are reviewed and I establish an intuitive physical understanding directly related to measurement procedures. To give you some hands on experience, I present a derivation of Kraus representations for simple models. At the end, I give an overview about current research interests and issues yet to be resolved.

### Friday, October 19, 2018, 2pm (26C/401)

Jonas Becker:

One approach to paper quality plots with python's matplotlib

I will present only one of many possible approaches to plotting for journals. I will start with a few basics about image formats, fonts, LaTeX, pdf, etc. I will then go into boilerplate code I use for plotting. I look forward to hearing about your different approaches and discussing problems of mine. I will discuss concepts on the black board and perform some live coding on the projector.

### Friday, July 27, 2018, 2pm (MBPII 015)

Lukas Weber:

Surface critical behavior in the O(n) model with Landau theory and epsilon expansion

### Friday, June 1, 2018, 2pm (MBPII 015)

Xingjie Han:

A brief introduction to cuprates

### Friday, May 4, 2018, 2pm (MBPII 015)

Timo Reckling:

Doping a Mott insulator: physics of high-temperature superconductivity

The seminar will be based on a review paper (same title) by P. Lee, N. Nagaosa and X. Wen, which is published as: Rev. Mod. Phys. 78, 17 (2006).

We will cover chapters I-V of the paper.

### Friday, April 20, 2018, 2pm (MBPII 015)

Jonas Becker:

Fractionalized Excitations in Topological Spin Liquids

The seminar will be based on the review paper "Exotic quantum phases and phase transitions in correlated matter" by Fabien Alet, Aleksandra M. Walczak, Matthew P.A. Fisher, arXiv:cond-mat/0511516

Published in https://doi.org/10.1016/j.physa.2006.04.003 (Elsevier)

### Friday, April 6, 2018, 2pm (26 C 401)

Giulio Schober:

Ab initio materials physics and microscopic electrodynamics of media

We scrutinize the traditional macroscopic theory of electrodynamics in media from a modern first-principles point of view. Our main result is that the traditional, phenomenological theory has to be replaced with a theory which is derived from first principles (i.e., many-body quantum mechanics), and which is consistent with the common practice in ab-initio materials science.

### Friday, February 9, 2018, 2pm (26 C 401)

Jan Diekmann:

The seminar will be based on the historical paper by J. Kondo: Resistance Minimum in Dilute Magnetic Alloys, Prog. Theor. Phys., **32**:37, 1964

### Friday, February 2, 2018, 2pm (26 C 401)

Jovan Odavić:

Statistical tools for detecting power law distributions

We present a set of statistical tools based on maximum likelihood estimators and Kolmogorov-Smirnov statistics that give a statistically accurate measure of power law distributions in empirical data. These methods supersede common graphical identification of such distributions.The seminar will be based on the paper: SIAM Review **51**, 661-703 (2009)

### Friday, January 12, 2018, 2pm (26 C 401)

Lisa Markhof:

Functional renormalization group in one dimension with MPI

### Friday, December 8th, 2017, 2pm (26 C 401)

Niklas Dittmann:

Introduction to time-dependent density-functional theory

### Friday, December 1st, 2017, 2pm (26 C 401)

Carsten Lindner:

Time dynamics of open quantum system

### Friday, November 10th, 2017, 2pm (26 C 401)

Timo Reckling:

Functional renormalization group in 2D lattice Hubbard models

### Friday, October 27th, 2017, 2pm (26 C 401)

Stephan Heßelmann:

Determinantal Quantum Monte Carlo simulations for fermionic lattice models

I will review the basic formulation of Determinantal Quantum Monte Carlo (DQMC), which is based on the introduction of bosonic auxilliary fields via a discrete Hubbard-Stratonovitch decomposition to decouple the fermionic interaction term. I will discuss all the necessary numerical steps and use the one band Hubbard model as prototypical example for a fermionic lattice model of interest, as well as comment on the advantages and limitations of DQMC compared to other available methods.

### Friday, October 20th, 2017, 2pm (26 C 401)

Jannis Ehrlich:

Introduction to the GW approximation in many-body perturbation theory

During the last decade the GW approximation has been applied successfully to a broad range of real materials, resulting in more realistic band structures in contrast to DFT. While the latter is a mean field theory, GW originates from an expansion of the self energy of the many body system in terms of the one particle Green function.

In this talk I will derive the set of the Hedin Equations which are a self consistent set of equations describing the full electronic problem. By one iteration of those equations the GW-self energy can be obtained. I will further give a rough description how it is implemented in the Jülich GW-code "spex".

### Friday, September 8th, 2017, 2pm (26C 402)

Julian Mußhoff:

Introduction to Dynamical Mean-Field Theory (DMFT)

### Friday, August 25th, 2017, 2pm (26C 402)

Patrick Emonts:

Programming experience (makefiles/debuggers etc.)

### Friday, August 11th, 2017, 2pm (26C 402)

Kim Lind Pedersen:

The physics behind www.quantumgraphs.com

### Friday, July 28th, 2017, 2pm (26C 402)

Philippe Suchsland:

Applying neural networks in condensed matter physics

### Friday, July 14th, 2017, 2pm (26C 402)

Jovan Odavić:

Density-functional theory for lattice systems

### Friday, June 23rd, 2017, 2pm (26C 402)

Gregor Michalicek:

Introduction to density-functional theory (DFT)

### Friday, June 2nd, 2017, 2pm (26C 402)

Andishe Khedri:

Introduction to the numerical renormalization group (NRG)

### Friday, May 19th, 2017, 2pm (26C 402)

Jonas Becker:

Concluding remarks on the stochastic series expansion (SSE)

### Friday, May 5th, 2017, 2pm (26C 402)

Cornelie Koop:

Measurement in the stochastic series expansion (SSE)

### Friday, April 21st, 2017, 2pm (26C 402)

Patrick Emonts:

Introduction into stochastic series expansion (SSE)

### Friday, March 3rd, 2017, 2pm (26C 402)

Katharina Eissing :

Presentation of FRG (functional renormalization group) in a simple and instructive way