I will give an overview of recent work on minimal models for quantum chaos in spatially extended many-body quantum systems, describing simple, solvable models. The detailed study of generic quantum systems -- ones without exact or approximate conservation laws -- goes back at least as far as investigations of highly-excited states in nuclei in the 1950s. It saw revivals in the 1980s with work on systems such as quantum billiards, that have only a few degrees of freedom, and also in the context of mesoscopic conductors. It is attracting renewed current interest with a focus on many-body systems that are spatially extended. The study of dynamics in spatially many-body systems introduces new questions that do not arise in finite systems such as quantum billiards, or in extended single- particle systems, such as mesoscopic conductors. These questions concern the dynamics of quantum information and the approach to equilibrium. I will discuss for minimal models both these new questions and established ways of characterising generic quantum systems via statistical properties of spectra. Based on: A. Chan, A. De Luca, and J. T. Chalker, Phys. Rev. Lett. 121, 060601 (2018) and Phys. Rev. X 8, 041019 (2018)
Topological insulators are a novel class of materials that exhibit a novel state of matter – while the inside (bulk) of the materials is electrically insulating, their surface is metallic. This effect occurs because the band structure of the materials is topologically different (in a mathematical sense) from the outside world. This talk describes our discovery of this type of behavior while studying the charge transport properties of thin, two-dimensional layers of the narrow-gap semiconductor HgTe. These layers exhibit the quantum spin Hall effect, a quantized conductance which occurs when the bulk of the material is insulating. Using various tricks one can show that the transport occurs along one-dimensional, spin-polarized channels at the edges of the sample. Also thicker HgTe samples can be turned into topological insulators, but now the surface states are two-dimensional metallic sheets. The metal in these sheets is rather exotic in that the band structure is similar to that encountered for elementary particles – the charge is carried by so-called Dirac fermions. This means that experiments on these layers can be used to test certain predictions from particle theory that are difficult to access otherwise. As an example, I will describe experiments where a supercurrent is induced in the surface states by contacting these structures with Nb electrodes. AC investigations indicate that the induced superconductivity is strongly influenced by the Dirac nature of the surface states. We present strong evidence for the presence of a gapless Andreev mode in our junctions. Finally, by playing with the strain in the layers, we can turn HgTe into a Dirac semimetal, which exhibits the ‘axial anomaly’ known from particle physics when the Fermi level is tuned to the Dirac points.
Optomagnonics studies the quantum-coherent coupling of light to collective magnetic excitations in solid state systems. The magnetic material hosting the magnetic excitations can be also used as an optical cavity if patterned appropriately. This not only enhances the magnon-photon coupling (making these systems promising for applications in quantum technologies) but also allows studying cavity-modified light-matter interaction in a novel platform. In my talk I will go over the basics of cavity optomagnonics and present results on recent theory developments in my group, including optomagnonics with magnetic textures, optical heralding of magnon Fock states, and antiferromagnetic cavity optomagnonics.
Spin liquids are collective phases of quantum matter that have eluded discovery in correlated magnetic materials for over half a century. In theory and experiment, there exist many beautiful models and plenty of promising candidate materials for their realization. However, one of the central challenges for the clear diagnosis of a quantum spin liquid (QSL) phase has been to understand the effect of disorder. From that perspective, this talk discusses three different roles of disorder: First, as a nuisance which obscures clear signatures of a QSL; Second, as a powerful new probe to uncover subtle QSL correlations; and Third, as a novel tuning parameter giving rise to qualitatively new disorder-QSL types. After a general introduction, the talk will focus on recent developments in Kitaev Spin Liquids.
Randomness leads to modification of the properties of low-dimensional spin-systems. Our study of time-reversal invariant quenched disorder on some frustrated spin-systems with non-collinear magnetic and spin-liquid ground states reveals how disorder acts to the detriment of the ordering, interferes with the topological properties of the ground state and causes the emergence of glassy behaviour. As examples, we have considered triangular lattice Heisenberg magnets and U(1) Dirac spin-liquids and found a pattern of disorder-induced destruction of the background order in two spatial dimensions. These results parallel the experimental efforts to uncover the low-temperature behaviour of various frustrated magnets.
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.