Hydrodynamics is a powerful framework for large-wavelength phenomena in many-body systems. It was extended recently to include integrable models, giving "generalised hydrodynamics". In this talk, I will review fundamental aspects of the hydrodynamics of integrable systems, with the simple examples of the quantum Lieb-Liniger and the classical Toda models. I will discuss a recent cold-atom experiment that confirmed the theory, and, if time permits, show some of the exact results that can be obtained with this formalism, such as exact nonequilibrium steady states and exact asymptotics of correlation functions at large space-time separations in Gibbs and generalised Gibbs states.
Causal Dynamical Triangulations (CDT) is a candidate theory for quantum gravity, formulated nonperturbatively as the scaling limit of a lattice theory in terms of piecewise flat (triangulated) spacetimes. From a technical and conceptual perspective, an important feature of this approach is its elegant resolution of the problem of how to treat the diffeomorphism symmetry of the classical theory in the full, background-free quantum theory. This has enabled the concrete computation of geometric observables in a highly nonperturbative, Planckian regime, an important step in putting quantum gravity on a quantitative footing, and understanding the structure of quantum spacetime. While the need to find quantum observables describing this regime is common to all approaches, CDT quantum gravity provides a concrete testing ground for implementation and measurements. In particular, a new notion of quantum Ricci curvature has opened a new window on some of the counterintuitive properties of quantum geometry.
Two-dimensional superconductors with broken time-reversal symmetry have been predicted to support topologically protected chiral edge states, providing a superconducting counterpart to the quantum Hall effect in semiconductors. The edge states carry charge-neutral quasiparticles, coherent superpositions of electrons and holes referred to as "Majorana fermions". We present an overview of electrical and thermal probes of the superconducting edge states, focusing on unique signatures of their Majorana nature and on applications for topological quantum computation. In particular, we show how topological qubits can be braided by injecting them into the conducting edge of a superconductor.
Connecting theoretical models for exotic quantum states to real physical systems is a key goal in the study of quantum materials. Among such theoretical models, a “toy model” is one made deliberately simplistic in order to demonstrate new physical concepts and their underlying mechanisms. Such models have proven to be tremendously successful in offering insight in to new condensed matter phenomena including those involving electronic topology and correlation. We describe here our recent progress in experimentally realizing “toy model” quantum materials which, in analogy to their theoretical counterparts, are designed to capture simple model systems by lattice and superlattice design. We detail developments in synthesizing and studying magnetic and superconducting materials that allow for new connections to long-standing predictions for unusual topological electronic phases. We close with a perspective for realizing further toy model systems in complex material structures.
Ultracold atoms in optical lattices constitute a versatile platform to study the fascinating phenomena of gauge fields and topological matter. Periodic driving can induce topological band structures with non-trivial Chern number of the effective Floquet Hamiltonian and paradigmatic models, such as the Haldane model on the honeycomb latticce, can be directly engineered. In this talk, I will report on our recent experiments, in which we realized new approaches for measuring the Chern number in this system and map out the Haldane phase diagram. This includes time-resolved Bloch-state tomography allowing for the observation of a dynamical linking number after a quench as well as the application of machine learning techniques to analyse experimental data. In the future, the combination of gauge fields with a quantum gas microscope will allow accessing new regimes such as fractional Chern insulators.
Developing a theory of activated dynamics is one of the most challenging problems of disordered systems. Activated glassy dynamics is central in many different contexts both in physics and beyond, e.g. in computer science and biology. In this talk, after a general introduction, I will describe recent research works aimed at characterising the activated dynamics of mean-field glassy systems. In particular I will discuss numerical results on the random energy model and variants, and analytical results on the organization of barriers in the p-spin spherical model.