Scientific Series

Experimentalists have recently been able to engineer non-trivial topological band structures using ultracold atoms in optical lattices.

Motivated by ongoing experimental efforts to tune interactions, we explore the interplay between strong correlations and topology in these systems. Focusing on the Haldane-Hubbard honeycomb model as an example, we show that its strongly interacting Mott limit exhibits various chiral magnetic orders, including a wide regime of triple-Q tetrahedral order. Incorporating an additional third-neighbour hopping frustrates and ultimately "quantum-melts" the tetrahedral magnetic order. From analysing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid with gapped semion excitations. Our numerical results suggest that this frustration induced melting may be realised as an exotic continuous quantum phase transition. Finally, we discuss recent results which point toward a common mechanism of realising chiral spin liquids through the continuous melting of non-coplanar magnetic "parent" states.

The space of causal diamonds recently brought to attention by de Boer et al. and Czech et al. provides an organizing principle for the dependence of entanglement entropy in conformal field theories on the spatial subregion considered. I will show that the inclusion relation of causal diamonds does not give rise to a consistent notion of a causal structure and thus does not provide an alternate metric on this space. I will also show that the entanglement entropy of ball shaped regions is not enough to reconstruct the areas of higher dimensional bulk surfaces in a static geometry. Instead, I will provide a new direction for the reconstruction of the areas of bulk surfaces from boundary data in holography, using the shape derivatives of the entanglement entropy of nearly ball shaped regions.

I will discuss the properties, and constraints on, new light

particles, which appear in many extensions of the Standard Model. An

especially well motivated example is the QCD axion, and I will show how

its mass and couplings can be extracted at high precision. I will also

discuss its properties at finite temperature, and possible distinguishing

features if it makes up dark matter. More generally, strong constraints on

the couplings of new light particles to the Standard Model come from their

production in the hot cores of stars, and the effect on stellar cooling.

The large electron density in stellar cores gives large thermal effects,

and I will show how these can parametrically change the production rates

compared to a 'tree level' calculation.

We argue that moduli stabilization severely constrains the evolution following transitions between weakly coupled de Sitter vacua and can induce a strong selection bias towards inflationary cosmologies. We carefully discuss gravitational vacuum decays and resolve a naive sign ambiguity in the exponential of the decay rate. Equipped with this clear understanding of vacuum decay we then turn towards constraints on the cosmological evolution after transitions in weakly coupled flux compactifications. The energy density of domain walls between vacua typically destabilizes Kahler moduli and triggers a runaway towards large volume. This decompactification phase can collapse the new de Sitter region unless inflation lasts for more than roughly 60 efolds. High scale inflation is vastly favored. Our results illustrate the necessity to understand inflationary initial conditions at least at a basic level, before making predictions in the landscape.

In order to solve the problem of quantum gravity, we first need to pose the problem. In this talk I will argue that the problem of quantum gravity arises already in the domain of quantum mechanics and the relativity principle. Specifically, the relativity principle implies that the concept of inertial motion should extend also to those systems that are in quantum superpositions of inertial motions. By contrast, relativistic quantum field theory only considers the point of view of classical observers in states of definite relative motion (i.e. the observers of a quantum field do not include inertial observers in quantum superpositions). The problem is that, if we extend the class of inertial observers to include quantum observers, the manifold of local events becomes ill-defined, as `locality' itself becomes an observer-relative property of an event. Thus, the Relativity Principle and the Superposition Principle are jointly opposed to the concept of a space-time manifold of local events, and our understanding of relativistic quantum theory needs to be revised before gravity even enters the picture.

In this talk, I will address a major conceptual and technical concern of non-perturbative quantum gravity: the quantum superposition of causal structures of space-times. I will discuss a class of theories that can address the problem, their flaws, and their relation to general relativity.

The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. I will show how it can be generalised to arbitrary Lie groups, possibly non-compact. The result relies on the knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail. As an application, the Wigner-Eckart theorem will be used to construct an analogue of the Jordan-Schwinger representation, previously known only for finite-dimensional representations of the Lorentz group, valid for infinite-dimensional ones.

I will describe some of the recent progress in quantum query complexity, including super-quadratic separations between classical and quantum measures for total functions, a better understanding of the power of some lower bound techniques, and insight into when we should expect exponential quantum speedups for partial functions.

Recent explorations of the space of quantum field theories have provided novel topological and geometric information about this space. This voyage has resulted in the solution of some long-standing questions:  the computation of sought-after topological invariants (Gromov-Witten invariants) by a new physics-based approach, the first instance of exact correlation functions in a four-dimensional QFT and the unearthing of the action of dualities on the basic observables of three dimensional gauge theories.

Incommensurate charge order is a phenomenon in which the electrons in a crystal attempt to order with a period irrationally-related to that of

the lattice spacing. In the first half of this talk I will present recent work [1] in which we demonstrate that incommensurately charge-ordered systems can lower their free energy by forming quasicrystals: slices through higher-dimensional crystals with properties lying between  periodicity and disorder. The result potentially greatly increases the number of known, naturally-occuring quasicrystals from the two present examples, both of which were found in the same Siberian meteorite. In the second half I will present work from an ongoing experimental collaboration in which atomically-resolved scanning tunneling microscopy and atomic force microscopy on semiconducting monolayers of molybdenum diselenide (MoSe2) see conducting edge states along one-dimensional mirror twin boundaries. Remarkably, these edge states then develop their own energy gap via charge ordering [2]. We see a number of features suggestive of incommensurate order. By employing a simple analytical model we demonstrate that the effect is in fact a result of fine-tuning between charge ordering and quantum well physics coming from the small system size (on the order of thirty atoms).

[1] F. Flicker and Jasper van Wezel, Physical Review Letters 115, 236401

(2015), Natural 1D Quasicrystals from Incommensurate Charge Order

[2] S. Barja et al., Nature Physics 12, 751-757 (2016), Charge density

wave order in 1D mirror twin boundaries of single-layer MoSe2

I will explain and prove the statement of the title. The proof relies on a recent result of Slofstra in combinatorial group theory and the hypergraph approach to contextuality.

Based on http://arxiv.org/abs/1607.05870.

We consider conformal blocks of two heavy operators and an arbitrary  number of light operators in a 1+1 dimensional CFT with large central charge. Using the monodromy method, these higher-point  conformal blocks are shown to factorize into products of 4-point conformal blocks in the heavy-light limit for a class of OPE channels. This result is reproduced by considering suitable worldline configurations in the bulk conical defect geometry. We apply the CFT results to calculate the entanglement entropy of an arbitrary number of  disjoint intervals for heavy states. The corresponding holographic entanglement entropy calculated via the minimal area prescription precisely matches these results from CFT.