Collective Phenomena in Quantum Many-Body Physics: From Quantum Matter to Light

I will give an overview of how advances in engineering twisted two-dimensional materials with a “moiré superlattice” have revealed a rich playground for investigations into strongly-correlated electronic matter. I’ll introduce the theories deployed to explain some of the experimental puzzles that arise and give a personal view on the most promising lines of future work. Along the way, I will illustrate how some of these ideas echo historic themes in condensed matter physics, including Martin Gutzwiller’s visionary ideas on the many-body problem, and mention how they tie in to past and future activities at MPI-PKS.

I will review some aspects of dissipation engineering and describe our recent work demonstrating cavity-assisted cooling to target Floquet states.

How do isolated quantum systems reach thermal equilibrium? Starting from an out-of-equilibrium pure state, unitary dynamics prevents the system to become a thermal mixed state and yet the physics at late times resemble thermal equilibrium. This apparent conundrum is resolved by the Eigenstate Thermalization Hypothesis (ETH), which conjectures eigenstates of an ergodic quantum Hamiltonian to be locally indistinguishable from thermal states. This is achieved by predicting the matrix elements of local observables to smoothly depend on the involved energies in a way that ensures thermalization. In this talk I will give a brief introduction to the ETH and its consequences, focusing in particular on the dynamics of correlation functions. In order to capture the latter in full generality, recently an extension, dubbed full ETH, has been proposed. After introducing full ETH I will sketch, how it allows for a systematic characterization of arbitrary correlation functions in terms of simple elementary building blocks by borrowing tools from the mathematical field of free probability.

In 1929, the Swiss physicist Felix Bloch studied the Schrödinger equations with a periodic potential and discovered that the solution can be expressed as plane waves modulated by periodic functions. This result is known as “Bloch’s theorem” and constitutes a foundational building block of condensed matter physics. In this talk, I will introduce the Bloch states and their energy eigenvalues which give rise to the electronic band structure of crystalline solids. More recently, there is an increased interest in the properties of the Bloch states, such as the Berry curvature and the quantum metric. I conclude by showcasing where these properties play an important role in modern condensed matter physics, e.g., in topological insulators and superconductivity in non-dispersive bands.

All magnetically ordered states of materials form by the collective ordering of spins, and spins are quantum mechanical objects, so one might think that quantum magnetism is really the only kind there can be. Strictly that's true; however, many magnets exhibit only weak entanglement between neighbouring spins, and thus can be thought of as approximately classical objects. In this lecture I will: (i) give an introduction to this distinction between classical and quantum magnetism; (ii) give rules of thumb for when quantum magnetism is likely to be energetically favourable; and (iii) give a couple of basic examples of the kind of states that result.

Magnetism in solids emerges from the interplay between quantum mechanics and many-body interactions. The study of transport properties of magnetic systems can provide significant insights into new phases of matter, exotic excitations, and their potential functionalities in technology innovation. This talk is a perspective based on my recent exploration of magnetic transport, from the aspects of geometric frustration, band topology, and dissipative dynamics, and connecting theoretical concepts to experimentally observable phenomena. I will focus on the first two aspects with the examples of the emergence of spin diffusion in the frustrated triangular-lattice magnet in the intermediate-temperature regime and the topological magnon polarons in van der Waals magnets and the resulted thermal Hall effect. Finally, I will briefly introduce the dissipative dynamics of a spin chain as an open quantum system and the non-Hermitian skin effect therein.

In this lecture I will show how to derive from phenomenological models the coupling between magnons and cavity photons in different frequency regimes, and discuss experimental signatures.