Talks

Compatibility of asymptotic safety with UV-completions of matter theories may constrain the underlying microscopic dynamics of quantum gravity. Within truncated RG-flows, a weak-gravity bound originates from the loss of quantum scale-invariance in the matter system. Further constraints could arise when linking Planck-scale to electroweak-scale dynamics. Within the constrained region, gravitationally induced scale-invariance could UV-complete the Standard Model, and moreover explain free parameters such as fermion masses and gauge couplings.

I will describe the recently developed bimetric theory of fractional quantum Hall states. It is an effective theory that includes the Chern-Simons term that describes the topological properties of the fractional quantum Hall state, and a non-linear, a la bimetric massive gravity action that describes gapped Girvin-MacDonald-Platzman mode at long wavelengths. The theory reproduces the universal features of the chiral lowest Landau level (LLL) FQH states that lie beyond the reach of pure Chern-Simons theory, such as the projected static structure factor and the Girvin-MacDonald-Platzman algebra. The action of particle-hole transformation on the theory is particularly transparent. Familiar quantum Hall observables acquire a geometric interpretation in the bimetric language

Quantum error correction -- originally invented for quantum computing -- has proven itself useful in a variety of non-computational physical systems, as the ideas of QEC are broadly applicable. In this talk, I'll mention a few examples of error correction in the wild, including the recent discovery that the AdS/CFT correspondence implements quantum error correction.  We will then study the hypothesis that any local bulk operator in AdS can be reconstructed using only a causally disconnected subregion of the CFT.  This hypothesis has been proven under the assumption that error correction in AdS/CFT is exact, but this assumption is not expected to be true.  Fortunately, recent advances in the theory of approximate quantum error correction have emerged.  We will review these results on recoverability and approximate quantum error correction, as well as AdS/CFT and the so-called entanglement wedge reconstruction hypothesis.  We will then prove the entanglement wedge hypothesis robustly and find an explicit formula for reconstructed bulk operators.  If time permits, we will explore a generalization of the theory of universal recovery channels to the case of finite-dimensional von Neumann algebras.

Our sense of smell is extraordinarily good at molecular recognition: we can identify tens of thousands of odorants unerringly over a wide concentration range. The mechanism by which this happens is still hotly debated. One view is that molecular shape governs smell, but this notion has turned out to have very little predictive power. Some years ago I revived a discredited theory that posits instead that the nose is a vibrational spectroscope, and proposed a possible underlying mechanism, inelastic electron tunneling. In my talk I will review the history and salient facts of this problem and describe some recent experiments, both on fruit flies and on humans, that go some way towards answering the question. 

BCS bogoliubon excitations, quantum Hall effect (QHE) and Landau levels (QHE handout)

Conventional quantum processes are described by quantum circuits, that represent evolutions of states of systems from input to output. In this seminar we consider transformations of an input circuit to an output circuit, which then represent the transformation of quantum evolutions. At this level, all the processes complying to admissibility conditions have in principle a physical realization scheme. The construction of a hierarchy of transformations of transformations, however, can proceed arbitrarily far, and in the higher orders one encounters admissible functions that have indefinite causal structures. These give rise to questions about possible realization schemes. Still, many of the maps in the hierarchy can be proved to have a realistic physical interpretation. In order to study the hierarchy, we introduce a simple rule for constructing new types of maps from known ones, and show how the tensor product can be rephrased in terms of the new rule. We use the hierarchy of types to introduce a partial order, which allows us to prove properties of maps by induction. We will then use induction proofs to discuss the characterisation of mathematically admissible maps at every level. We show an important structural result for a subclass of higher-order maps, and we conclude with the open question of their physical achievability.

Quantum critical points (QCP) beyond the Landau-Ginzburg paradigm are often called unconventional QCPs. There are in general two types of unconventional QCP: type I are QCPs between ordered phases that spontaneously break very different symmetries, and type II involve topological (or quasi-topological) phases on at least one side of the QCP. Recently significant progress has been made in understanding (2+1)-dimensional unconventional QCPs, using the recently developed (2+1)d dualities, i.e., seemingly different theories may actually be identical in the infrared limit. One group of dualities between unconventional QCPs have attracted particular interests in the field of condensed matter theory. This group of dualities include the so called deconfined QCP between the Neel and valence bond solid phases, and the topological transition between a bosonic topological insulator and a trivial Mott insulator. Each of the transitions mentioned above is also "self-dual". This group of dualities make extremely powerful predictions for numerical test. We will review the theoretical aspects and most recent numerical evidences for these new results.