Department of Physics • University of Cologne

Textbook quantum criticality refers to phenomena which originate in states which scale-invariant in both space and time, occurring at continuous zero-temperature phase transitions. Various experimental findings have raised interest in local forms of quantum criticality, where scale invariance in space in either absent or irrelevant. Prominent examples include variants of the Mott metal-to-insulator transition in a number of strongly correlated electron compounds. After an extended introduction, I will discuss one of the simplest cases, namely the bandwidth-tuned Mott transition in a single-band setting. Recent transport studies, both theoretical and experimental, near this transition have uncovered - surprisingly - apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. I will argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, scale-invariant (i.e. power-law) solutions which had been overlooked before. It is this incoherent power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. I will discuss the role of magnetic frustration in these phenomena, non-local corrections, and broader implications for the phenomenology of bad metals.

Only the Speed of Light limits You? - Discrimination and its impact on the academic field of physics Everyone who is good enough in physics can work in the academic field, no matter what their identity is besides that, right? We do not have any issues with discrimination, or do we? Is our study and work environment really benefiting everyone equally? Or are people marginalized here as well – and if so, what is going on? And what can we do about it? The talk will be given by Prof. Tomas Brage. He has a very successful career in physics and is currently a physics professor at the Division of Mathematical Physics of the Department of Physics at Lund University. Besides all his publications in this field, he also does research concerning “Gender and Physics”. He will inform us about numbers, bias, and stereotypes regarding gender, and their influence on physics. After his talk, we can also ask questions and have a discussion about the topic.

Topological phases were discovered in condensed matter physics and recently extended to classical physics such as topological mechanical metamaterials. Their study and realization in soft-matter and biological systems has only started to develop. In this talk we discuss how topological phases may determine the behavior of nonlinear dynamical systems that arise, for example, in population dynamics. We have shown that topological phases can be realized with the anti-symmetric Lotka-Volterra equation (ALVE). The ALVE is a paradigmatic model system in population dynamics and governs, for example, the evolutionary dynamics of zero-sum games, such as the rock-paper-scissors game [1], but also describes the condensation of non-interacting bosons in driven-dissipative set-ups [2]. We have shown that for the ALVE, defined on a one-dimensional chain of rock-paper-scissors cycles, robust polarization emerges at the chain’s edge [3]. The system undergoes a transition from left to right polarization as the control parameter passes through a critical value. At the critical point, solitary waves are observed. We found that the polarization states are topological phases and that this transition is indeed a topological phase transition. Remarkably, this phase transition falls into symmetry class D within the “ten-fold way” classification scheme of gapped free-fermion systems, which also applies, for example, to one-dimensional topological superconductors. Beyond the observation of topological phases in the ALVE, it might be possible to generalize the approach of our work to other dynamical systems in biological physics whose attractors are nonlinear oscillators or limit cycles. [1] J. Knebel, T. Krüger, M. F. Weber, and E. Frey, Phys. Rev. Lett. 110, 168106 (2013). [2] J. Knebel, M. F. Weber, T. Krüger, and E. Frey, Nature Communications 6, 6977 (2015). [3] J. Knebel, P. M. Geiger, and E. Frey, Phys. Rev. Lett. (in press) [arXiv:2009.01780].

The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics. The measurement of the Hall conductivity of a two-dimensional electron system showed that electrical conduction can be precisely defined only in terms of fundamental constants. But, what happens to the QHE in three dimensions? At a first glance, the answer seems straightforward and sobering: The quantization of the Hall conductivity gets destroyed. This has led to the general conjecture that quantum-Hall physics is exclusive to two dimensions. However, we show that the Hall effect of genuine three-dimensional (3D) metals is actually deeply related to the QHE and can be understood from quantum Hall physics. We propose that - as a general rule - plateau-like features in the Hall conductivity of 3D electron systems are precisely given by the conductance quantum, scaled by the Fermi wave vector of the electrons along the magnetic field direction.

Everyone who is good enough in physics can work in the academic field, no matter what their identity is besides that, right? We do not have any issues with discrimination, or do we? Is our study and work environment really benefiting everyone equally? Or are people marginalized here as well – and if so, what is going on? And what can we do about it? The event will be with Sherard Robbins, a development consultant, author, and CEO of Visceral Change. He will address the topic of “Racism and Physics” and present us some background information and numbers about it. There will also be space for discussions: How does it affect our work environment and what can we do about it?