Department of Physics • University of Cologne

Machine learning techniques can boost the exploration of complicated phase diagrams in many-body systems. To date, most studies are tied to situations involving only one phase transition and one order parameter. Systems accommodating multiple phases of coexisting and competing orders remain largely unexplored. Using Support Vector Machines (SVMs) we focus on multipolar orders and their tensorial order parameters, whose identification is difficult with traditional methods. The key property that allows one to make progress is the interpretability of the decision function, from which the physical order parameter can be deduced. Furthermore, we discuss a second intrinsic parameter of the SVM, the bias, which allows one to make an unsupervised graph analysis of the topology of the phase diagram. We illustrate our tool for the classical XXZ model on the frustrated pyrochlore lattice. Unexpectedly, the machine could also learn local constraints hinting at various types of spin liquids resulting in a complete classification of all types of behavior for this model.

Layered materials host various collective quantum states such as intertwined electronic spatial orders, superconductivity or topological spin liquids. I will present two examples from our recent work, which are concerned with then manipulation of such collective quantum states. The first example is the laser-induced metal-insulator transition of 1T-TaS2, which is currently discussed intensively in relation to a somewhat enigmatic hidden state. Our experiments reveal the microscopic nature of this hidden state and show that the non-thermal metal-insulator transition of 1T-TaS2 corresponds to a transition between two long-range ordered electronic crystals. The second example is alpha-RuCl3 - a candidate material for Kitaev magnetism and the corresponding spin-liquid ground state. However, at ambient pressure and low temperatures this material does not exhibit a spin-liquid phase, but antiferromagnetic long-range order. We discovered a high-symmetry rhombohedral phase of alpha-RuCl3 at non-ambient pressure, which may indeed support a Kitaev spin-liquid ground state.

Fully quantum fluctuation relations incorporate coherence and quantum correlations, but typically require explicit modeling of components that more traditional approaches (both classical and quantum) only treat implicitly. Such components include the system that delivers the work, as well as the system that imposes the external control. In this project, we strive to mimic the general machinery of fully quantum fluctuation relations in a purely classical phase space setting, and within this construction derive classical counterparts to various fully quantum fluctuation relations. One goal is to understand the effects of introducing explicit batteries and external controls in the classical scenario, and how this relates to standard classical approaches. A further aim is to enable a comparison between fully quantum fluctuation relations and classical fluctuation relations on a more equal footing.

We will first review spectral flow and its application to bulk and boundary properties of the quantum Hall effect. We will then introduce the so-called KO-valued spectral flow, defined in joint work with Alan Carey, Matthias Lesch and Adam Rennie, and how it can be used to recover the classification of topological insulators and superconductors by Kennedy and Zirnbauer. Time permitting, we will then present recent joint work with Johannes Kellendonk and Adam Rennie, which uses the Cayley transform on Hilbert C*-modules to generalise many of these ideas and gives analogous results to recent work by Alldridge, Max and Zirnbauer.

Domain walls naturally arise whenever a symmetry is spontaneously broken. They interconnect regions with different realizations of the broken symmetry, promoting structure formation from cosmological length scales to the atomic level. In my talk, I will present 1D spin textures and domain walls with intriguing physical properties, which emerge in spin-spiral multiferroics and chiral magnets and which hold great promise for nanoelectronics and spintronics applications. In particular, I will discuss that a wide variety of new domain walls occurs in the presence of spatially modulated domain states. In contrast to domain walls in conventional ferroics, such domain walls exhibit a well-defined inner structure, which—analogous to cholesteric liquid crystals—consists of topological disclination and dislocation defects. Similar to the magnetic skyrmions, the domain walls can carry a finite topological charge, permitting an efficient coupling to spin currents and contributions to a topological Hall effect. Our studies establish domain walls in chiral magnets as functional nano-objects with non-trivial topology, opening the door to innovative device concepts in information and communication nanotechnology.