Department of Physics • University of Cologne

We shall briefly review the present day situation with unexpectedly high-temperature superconductivity in FeSe monolayers on SrTiO_3 (FeSe/STO), the main experimental results, the electronic structure (ARPES data and calculations) and possible mechanisms of Tc enhancement. We shall discuss the origin of unusual shallow conduction bands in FeSe/STO with quite small values of Fermi energy, which we attribute to the increasing electronic correlations (as compared to the bulk FeSe). We shall briefly review the idea of Tc enhancement due to FeSe electrons interactions with high - energy optical phonons of STO, stressing the importance of antiadiabatic effects, which will be discussed within the Eliashberg - McMillan approach.

In the past decade we have witnessed enormous progress in experiments that consist of placing magnetic atoms at predetermined positions on substrates and building magnetic nanostructures, one atom at a time. The interactions between magnetic moments are mediated by the conduction electrons through a mechanism understood in terms of a theory developed decades ago by Ruderman, Kittel, Kasuya, and Yosida, dubbed "RKKY theory", which applies when the spins are classical. The quantum nature of the electronic spin introduces another degree of complexity and competition with other quantum phenomena: the Kondo effect. This competition is quite subtle and non-trivial, and can only be studied by numerical means. We explore these phenomena on different lattice geometries in 1,2 and 3 dimensions by introducing an exact mapping onto an effective one-dimensional problem that we can solve with the density matrix renormalization group method (DMRG). We show a clear departure from conventional RKKY theory and important differences that can be attributed to dimensionality and geometry. In particular, for the square and cubic lattices at half filling, Kondo physics dominates even at short distances, while the ferromagnetic RKKY state is energetically unfavorable, translating into a finite range for the RKKY interaction. In the case of larger spin S=1, RKKY correlations can coexist with (partial) screening.

Chiral spin liquids are highly entangled phases of interacting spins that break time reversal and inversion symmetries, but lack conventional magnetic order even at zero temperature. While chiral spin liquids have not been unambiguously observed in nature yet, they are expected to exhibit exotic properties following from a spectrum of fractional excitations. Theoretically, chiral spin liquids are often described by strongly coupled gauge theories which are hard to tackle analytically beyond mean-field approximations. In this talk, I will describe controllable approaches that allow us to understand various chiral spin liquids starting from lower-dimensional building blocks, namely arrays or junctions of Heisenberg spin chains. In the case of junctions, I will discuss the connection between chiral spin liquids and chiral fixed points of boundary conformal field theory.

All animals and plants are associated to a huge number of microbes that live together with them or even within them. These microbes often have fundamental roles in the functioning of their hosts, from metabolic functions to defense against diseases. In many cases, a disease microbiome seems distinct from a healthy one. This multi-stability of microbiomes can be understood in terms of game theoretical models that describe the interactions between microbes, but it is challenging to assess the associated parameters from experimental data. On the other hand, many microbes will randomly vary in their abundance, such that stochastic models are more appropriate to describe them. In the most extreme case of neutral models, it is assumed that all microbes are identical. Such neutral models are widely used in theoretical ecology and they can be directly applied to the microbiomes of a wide variety of host organisms. Neutral models allow to identify key microbial types, which are not necessarily those that are found in particularly high abundance.

An exact formula for the temperature dependent Hall number of metals is derived. It is valid for nonrelativistic fermions or bosons, with an arbitrary potential and interaction. This dc transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.

Bacterial evolution of resistance to antibiotics is a major public health concern. Once prevalent, resistant strains can transmit among patients and become difficult to eradicate. However, ultimately, the resistant strains must originate from a de novo mutation or horizontal gene transfer event in a single bacterial cell. Using high-replicate experiments with Pseudomonas aeruginosa facing streptomycin as a model system, we quantified the probability that a single resistant cell establishes a large surviving lineage. Strikingly, this probability drops to near zero well below the standardly measured minimum inhibitory concentration (MIC) of the antibiotic. We show that this result can be explained by a simple model in which the antibiotic has partial inhibitory effects below the MIC, and each cell has an independent chance of establishment.

The discovery of topological insulators (TIs) has fuelled the search for novel topological phases of matter, by combining theory, computational high-throughput screening and experiments [1, 2]. From the experimental point of view, angle-resolved photoelectron spectroscopy (ARPES) has played a key role due its direct access to the material band structure. The advent of efficient spin detector, and ultrafast light source in the UV energy range, has further extended our capability to map also the vectorial spin texture and the out-of-equilibrium dynamics of the topological states. We have recently exploited these techniques to investigate TIs and several topological semimetal. We have tracked the evolution of the band structure of MoTe2 across the topological phase transition between a trivial semimetal and a type-II Weyl semimetal, as a function of the sample temperature [3]. Our results show that the presence of several bulk and surface states hamper a direct determination of the topological phase. However, the temporal dynamics of the photoexcited electrons reveals clear signatures of the Weyl point formation in the unoccupied band structure [4]. In the second part of my talk, I will show that optical excitation can be also used to alter the material band dispersion, as for the case of the nodal line semimetal ZrSiSe [5], which displays both spin polarized surface states and a bulk hidden spin polarization. [1] M. Z. Hasan and C. L. Kane, Reviews of Modern Physics 82, 3045 (2010). [2] B.-J. Yang and N. Nagaosa, Nature Communications 5, 1 (2014). [3] A. Crepaldi, et al., Phys. Rev. B 95, 041408 (2017). [4] A. Crepaldi, et al., Phys. Rev. B 96, 241408(R) (2017). [5] G. Gatti, et al., in preparation.

Quantum computers offer important speed-ups in the solution of a variety of problems. One of them is the simulation of quantum many-body systems, as they appear in atomic, condensed matter or high-energy physics, or quantum chemistry. Other, like SAT, are related to classical optimization problems. In this talk I will first review some of the quantum algorithms to simulate the equilibrium and dynamics of quantum many-body systems. Then I will present a hybrid quantum-classical algorithm to solve SAT problems with (relatively) small quantum devices.

Antrittsvorlesung.