Institute for Theoretical Physics • University of Cologne

Spin-polarized scanning tunneling microscopy at low temperature (8 K) and in high magnetic fields (6 T) is a powerful technique to investigate magnetic properties of individual nanoscale objects ranging in size form single atoms to several thousand atoms. I focus on the magnetization reversal and the spin-dependent electronic properties of bilayer Co, Fe-decorated Co and Fe islands on Cu(111). We find a novel noncollinear, helical magnetic order in the Fe islands, which is identified by a magnetic stripe contrast with a period of 1.28 nm. The high spatial resolution of the scanning tunneling spectroscopy reveals the significance of structural and electronic relaxation for the magnetic anisotropy and the spin-dependent transport properties of single islands. In an outlook I present first results from our new STM, which operates at 0.3 K in a vector magnetic field, on superconductivity of Pb monolayers and on the proximity effect.

A promising approach to realize quantum spin liquids is to enhance the spin-space symmetry from usual SU(2) to SU(N). While the SU(N) symmetry with a general N is proposed in ultracold atoms using nuclear spin degrees of freedom, its realization in magnetic materials is challenging. Here we propose a new mechanism by which the SU(4) symmetry emerges in the strong spin-orbit coupling limit. The spin-orbit coupling in d^1 transition metal compounds with edge-sharing anion octahedra leads to strongly bond-dependent hopping, which is apparently not SU(4)-symmetric. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

Non-relativistic quantum matter, as realized in ultracold atomic gases, continues to be a remarkably versatile playground for many-body physics. Experimentalists have exquisite control over temperature, density, coupling, and shape of the trapping potential. Additionally, a wide range of properties can be measured: from simple ones like equations of state to more involved ones like the bulk viscosity and entanglement. The latter has received much attention due to its connection to quantum phase transitions, but it has proven extremely difficult to compute: stochastic methods display exponential signal-to-noise issues of a very similar nature as those due to the infamous sign problem affecting finite-density QCD. In this talk, I will present an algorithm that solves the signal-to-noise issue for entanglement, and I will show results for strongly interacting systems in three spatial dimensions that are the first of their kind. I will also present a few recent explorations of the thermodynamics of polarized matter and other cases that usually have a sign problem, using complexified stochastic quantization.

The conceptual basis for a classical nonlocal generalization of Einstein's theory of gravitation is presented. The framework of general relativity is enlarged by the introduction of a preferred frame field; then, history dependence is introduced. Nonlocality --- in the sense of an influence ("memory") from the past that endures --- could be a natural feature of the universal gravitational interaction. Nonlocal gravity is formally analogous to the nonlocal electrodynamics of media. The nonlocal aspect of gravity can simulate dark matter. The implications of nonlocal gravity theory for the problem of dark matter in galaxies, clusters of galaxies, and cosmology are discussed. Special Colloquium honoring Friedrich Hehl's 80th birthday.

One hundred and fifty years ago, Maxwell's demon was first posed as a fundamental challenge to the newly developed field of statistical physics. Just two months later, Maxwell's paper "On governors" gave the first analysis of a feedback system. These two foundational works reflect the fundamental and practical aspects of control. Here, I will present an experiment that unites the two: using feedback to create `impossible' dynamics, we make a Maxwell demon that can reach the fundamental limits to control set by thermodynamics. We test - and then extend - Rolf Landauer's 1961 prediction that information erasure requires at least as much work as can be extracted from a system by virtue of information. These fundamental thermodynamic limits are benchmarks for evaluating the performance of practical information engines, such as those active within cells and other complex systems.

Algebraic order in two-dimensional systems with U(1) symmetry is destroyed by even the slightest deviation from detailed-balance conditions which are characteristic of thermal equilibrium. Such a violation of equilibrium conditions alters the interaction of topological defects in a drastic way: instead of being long-ranged and thus capable of holding together pairs of vortices and anti-vortices in the ordered phase, it becomes screened, and defects proliferate. Here, we show that the structure of defects and their interaction can equally dramatically be modified by the breaking of rotational symmetry. For sufficiently strong spatial anisotropy, the force that binds pairs of defects can even be enhanced up to parametrically large scales. As a consequence, the vortex-unbinding crossover in such finite-size systems exhibits peculiar universal behavior. In the thermodynamic limit, we argue that the modified structure of defects allows for a stable ordered phase. These results, which we obtain by analyzing the compact anisotropic Kardar-Parisi-Zhang (caKPZ) equation, are relevant for a wide variety of physical systems, ranging from strongly coupled light-matter quantum systems to recently proposed classical time crystals.

We study the contact process in the regime of small infection rates on scale-free networks evolving by stationary dynamics. A parameter allows us to interpolate between slow (static) and fast (mean-field) network dynamics. For two paradigmatic classes of networks we investigate transitions between phases of fast and slow extinction and in the latter case we analyse the density of infected vertices in the metastable state. This is joint work with Emmanuel Jacob (ENS Lyon) and Amitai Linker (Universidad de Chile).

Topological semimetals have recently been one of the most active topics in solid state physics, and provide an exceptionally fruitful meeting point for fields as diverse as chemistry, band structure calculations and high-energy field theory. This talk will discuss the observation of quantum anomalies in Weyl semimetals. These anomalies are rooted in an incompatibility of quantum mechanics and classical conservation laws. In particular, I will focus on recent measurements demonstrating the presence of the mixed axial-gravitational anomaly in Weyl semimetals. In contrast to earlier expectations, which would for example search for this phenomenon in the hydrodynamics of neutron stars, we used a conceptually simple thermoelectric transport experiment to find signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP.

A question that attracted a lot of attention in the past two decades is whether biologically relevant search strategies can be identified by statistical data analysis and mathematical modeling. A famous paradigm in this field is the Levy Flight Foraging Hypothesis. It states that under certain mathematical conditions Levy dynamics, which defines a key concept in the theory of anomalous stochastic processes, leads to an optimal search strategy for foraging organisms. This hypothesis is discussed very controversially in the current literature. I will review examples and counterexamples of experimental data and their analyses confirming and refuting it. Related to this debate is own work about biophysical modeling of bumblebee flights under predation thread and biological cell migration, both based on experimental data analysis, which I briefly outline.

The celebrated KPZ equation (Kardar, Parisi, Zhang, 1986) is an important milestone in statistical physics, originally introduced to describe the late time dynamics in two dimensional growth models. Over the last 30 years, the KPZ story has evolved in various interesting directions, making links on the way to different areas of physics and mathematics. This includes in particular the link to the famous Tracy-Widom distribution in random matrix theory. The story of KPZ is a very successful one, involving theoretical physics, mathematics and experiments--a fertile playground for interdisciplinary science. In this talk, I will review the evolution of the KPZ story, pointing out the important landmarks as I go along. At the very end, I will discuss some recent developments establishing a nice link between the KPZ height fluctuations and the edge physics in cold atom systems.