Conference

The topological Haldane model (THM) on a honeycomb lattice is a prototype of systems hosting topological phases of matter without external fields. It is the simplest model exhibiting the quantum Hall effect without Landau levels, which motivated theoretical and experimental explorations of topological insulators and superconductors. Despite its simplicity, its realization in condensed matter systems has been elusive due to a seemingly difficult condition of spinless fermions with sublattice-dependent magnetic flux terms. While there have been theoretical proposals including elaborate atomic-scale engineering, identifying candidate THM materials has not been successful, and the first experimental realization was recently made in ultracold atoms. Here we suggest that a series of Fe-based honeycomb ferromagnetic insulators, AFe2(PO4)2 (A=Ba,Cs,K,La) possess Chern bands described by the THM.

The 2D S = 1/2 square-lattice Heisenberg model is a keystone of theoretical studies of quantum magnetism. It also has very good realizations in several classes of layered insulators with localized electronic spins. While spin-wave theory provides a good understanding of the antiferromagnetic ground state and low-lying excitations of the Heisenberg model, an anomaly in the excitations at higher energy around wave-number q = (\pi, 0) has been diffi_cult to explain. At first sight, the anomaly is just a suppression of the excitation energy by a few percent, but it also represents a more dramatic shift of spectral weight in the dynamic spin structure factor from the single- magnon (spin wave) pole to a continuum. Recent neutron scattering experiments on the quasi-2D material Cu(DCOO)2_.4D2O (the best realization so far of the 2D Heisenberg model) were even interpreted as a complete lack of magnon pole at the anomaly; instead it was suggested that the excitations there are fractional (spinons) [1]. I will discuss recent quantum Monte Carlo and stochastic analytic continuation results pointing to the existence of fragile q~(\pi,0) magnon excitations in the Heisenberg model [2], which can be fractionalized by interactions competing with the nearest-neighbor exchange coupling. This phenomenon can be understood phenomenologically within a simple theory of magnon-spinon mixing.

Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified theories. Using new exact microscopic numerical simulations of superfluid 4He, we demonstrate for the first time an area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principles underlying its physical origin, and present an "entanglement equation of state" showing how it depends on the density of the superfluid.

In 1999, A. W. Hunt et al. discovered that all the NMR anomalies detected at the charge density wave (CDW) order transition Tcharge ~ 60 K of nearly non-superconducting La1.48Nd0.4Sr0.12CuO4 are shared by superconducting La1.88Sr0.12CuO4 (Tc ~ 30K) [1]. The unexpected finding inevitably led us to conclude that charge order must exist even in the superconducting La2-xSrxCuO4, sending a shockwave in the high-Tc community [2]. Subsequent search of charge order peaks based on scattering techniques, however, failed to detect additional evidence for charge order until very recently. In view of the recent confirmation of charge order in many superconducting cuprates by X-ray diffraction techniques, we revisit the old problem of charge order using newer NMR techniques that have become available in recent years.

In this talk I will introduce a relatively little-studied but intriguing family of metals, the delafossite series of layered oxides ABO2 in which the A site is occupied by Pd or Pt, and the B site by a transition metal. For reasons that are not perfectly understood, these materials have amazingly high electrical conductivity, with mean free paths of hundreds of angstroms (longer than even elemental copper or silver) at room temperature, growing to tens of microns at low temperatures. The electronic structure that yields these properties is in one way very simple, with a single half filled conduction band, but in another sense very rich, because the nearly free electrons originate mainly from the (Pt,Pd) layers in the crystal structure, while the adjacent transition metal oxide layers host Mott insulating states to which the conduction electrons also have some coupling. My group is interested in the delafossites for a number of reasons. Firstly, they are possible hosts for electronic transport at the crossover between ballistic and hydrodynamic regimes, which we investigate by fabricating size-restricted microstructures using focused ion beam techniques. As layered materials that can be cleaved at low temperatures, they are also well suited to study by angle resolved photoemission spectroscopy, and host a variety of interesting surface states in addition to a simple single-band bulk electronic structure. I will discuss our findings on non-magnetic PdCoO2, PtCoO2 and PdRhO2 and magnetic PdCrO2.

On the path towards quantum gravity we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). In this talk, I will erase that distinction. I encode gravity, along with other types of interactions, in the timeless configuration space of spatial fields, with dynamics obtained through a path integral formulation. The framework demands that boundary conditions for this path integral be uniquely given. Such uniqueness arises if a reduced configuration space can be defined and if it has a profoundly asymmetric fundamental structure. These requirements place strong restrictions on the field and symmetry content of theories encompassed here. When these constraints are met, the emerging theory has no non-unitary measurement process; the Born rule is given merely by a particular volume element built from the path integral in (reduced) configuration space. Time, including space-time, emerges as an effective concept; valid for certain curves in configuration space but not assumed from the start. When some notion of time becomes available, conservation of (positive) probability currents ensues. I will show that, in the appropriate limits, a Schroedinger equation dictates the evolution of weakly coupled source fields on a classical gravitational background. Due to the asymmetry of reduced configuration space, these probabilities and currents avoid a known difficulty of standard WKB approximations for Wheeler DeWitt in minisuperspace: the selection of a unique Hamilton-Jacobi solution to serve as background. I illustrate these constructions with a simple example of a quantum gravitational theory for which the formalism is applicable, and give a formula for calculating gravitational semi-classical relative probabilities in it. Although this simple model gives the same likelihood for the evolution of all TT gravitational modes, there is evidence that a slightly more complicated model would favor modes with the smallest eigenvalues of the Laplacian and thus drive towards homogeneity.

I will present results on the quantization of an FRLW model that utilises a Schrodinger-type evolution equation. In contrast to standard Wheeler--DeWitt-type quantisations, the quantum model resolves the classical singularity, exhibits a quantum bounce, and displays novel early-universe phenomenology. A global scale emerges because of a scale anomaly, and suggests an interesting scenario for quantum shape dynamics. I will give the details of the quantization procedure and show how these techniques can be used more generally for anisotropic models. I will end by speculating about how these techniques might be applicable to a genuine quantum shape model of the universe.

I will with simple examples from spatially homogeneous and isotropic cosmology illustrate the importance of respecting the global features of a state space for a given model when reformulating field equations to useful dynamical systems. In particular I will use examples from f(R) gravity and GR with a minimally coupled scalar field. In this context I will also illustrate how various dynamical systems methods, such as, e.g., monotonic functions, center manifold techniques, averaging methods, can yield a global understanding of the solution spaces as well as approximations, complementing, e.g., the slow-roll approximation.

I will show how the intrinsic definition of observables in relativity through dynamical similiarity (known as Shape Dynamics) leads to the continuation of Einstein's equations classically through the big bang singularity in simple cosmological scenarios. By appealing to general principles I argue that this is a generic feature, and that the singularity can be viewed as an artifact of the redundant description imposed by absolute length scales. I will then lay out some other welcome features of intrinsic relational systems, and discuss the broader questions raised by a theory of physics that is independent of physical dimensions such as mass and length.