Geometry and Topology in the Fractional Quantum Hall Effect
Duncan Haldane Princeton University
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Short Gamma-Ray Bursts and the Electromagnetic Counterparts of Gravitational Wave Sources
Edo Berger Harvard University
PIRSA:13090050 -
Self-organized topological state with Majorana fermions
Marcel Franz University of British Columbia
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Orbifolds and topological defects
Daniel Plencner Ludwig-Maximilians-Universität München (LMU)
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ΛCDM Large Scale Triumphs and Small Scale Challenges
Joel Primack University of California, Santa Cruz
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Geometry and Topology in the Fractional Quantum Hall Effect
Duncan Haldane Princeton University
The FQHE is exhibited by electrons moving on a 2D surface through which a magnetic flux passes, giving rise to flat bands with extensive degeneracy (Landau levels). The degeneracy of a partially-filled Landau level is lifted by Coulomb repulsion between the electrons, which at certain rational fillings, leads to gapped incompressible topologically-ordered fluid states exhibiting the FQHE. Successful model wavefunctions for FQHE states, such as the Laughlin and Moore-Read states, are surprisingly related to Euclidean conformal field theory, even though they are gapped incompressiible quantum fluids with a fundamental unit of area set by the area per magnetic flux quantum h/e. The model wavefunctions are parametrized by a continuously-variable Euclidean metric, just like the Euclidean conformal group of the cft to which they are related. This metric is fixed locally both by the form of the projected Coulomb interaction within the partially-filled Landau level, and by local gradients of the tangential electric field on the 2D surface, promoting it from a static flat metric fixed globally by the cft, to a dynamic local physical degree of freedom of the FQHE fluid with area-preserving zero-point fluctuations that leave an imprint in the ground-state structure function. The curious connection to cft appears to be that the Virasoro algebra plays a fundament role in both cft and FQHE, for apparently-unrelated reasons. In the FQHE it derives from a chiral "gravitional" (geometric) topologically-protected anomaly at the edge of the fluid that is also revealed in the entanglement spectrum of a cut through the bulk fluid. -
Alan Turing and the Enigma Machine
James Grime University of Cambridge
PIRSA:13100079Alan Turing was one of our great 20th century mathematicians, and a pioneer of computer science. However, he may best be remembered as one of the leading code breakers of Bletchley Park during World War II. It was Turing's brilliant insights and mathematical mind that helped to break Enigma, the apparently unbreakable code used by the German military. We present a history of both Alan Turing and the Enigma, leading up to this fascinating battle of man against machine - including a full demonstration of an original WWII Enigma Machine! -
Universal fault-tolerant quantum computation with only transversal gates and error correction
Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. It is known, however, that transversal gates alone cannot be computationally universal. I will show that the limitation on universality can be circumvented using only fault-tolerant error correction, which is already required anyway. This result applies to ``triorthogonal'' stabilizer codes, which were recently introduced by Bravyi and Haah for state distillation. I will show that triothogonal codes admit transversal implementation of the controlled-controlled-Z gate, and then demonstrate a transversal Hadamard construction which uses error correction to preserve the codespace. I will also discuss how to adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes. -
Slippery Waves: Brilliance Brings Blind Spots
Superfluidity and superconductivity are two remarkable phenomena in which, at low temperatures, materials abruptly gain the ability to flow without friction. Microscopic quantum theories of these phases of matter were constructed in blockbuster papers of Lev Landau (1940) and John Bardeen, Leon Cooper, and J. Robert Schrieffer (1957). The actual explanation of the flow, however, is rooted in a Einstein paper of 1924 that introduces a condensate, a quantum configuration describing a finite fraction of the particles in the system. Superfluidity can then be understood in terms of the wave function for this configuration, which necessarily extends over a finite fraction of the system. Neither blockbuster paper mentions Einstein or the crucial idea of a condensate wave function. The reasons for this omission are mooted. -
Electroweak Cogenesis and a CP Violating Higgs Boson
We propose a simple renormalizable model of baryogenesis and asymmetric dark matter generation at the electroweak phase transition. Our setup utilizes the two Higgs doublet model plus two complex gauge singlets, the lighter of which is stable dark matter. The dark matter is charged under a global symmetry that is broken in the early universe but restored during the electroweak phase transition. Because the ratio of baryon and dark matter asymmetries is controlled by model parameters, the dark matter need not be light. Thus, new force carriers are unnecessary and the symmetric dark matter abundance can be eliminated via Higgs portal interactions alone. The dark matter mass is also constrained within a window around the weak scale. One of the main predictions of this model is CP violating Higgs signals at the LHC and future colliders. -
Not so random walks in cosmology
Ravi Sheth University of Pennsylvania
I'll discuss a number of insights into the process of nonlinear structure formation which come from the study of random walks crossing a suitably chosen barrier. These derive from a number of new results about walks with correlated steps, and include a unified framework for the peaks and excursion set frameworks for estimating halo abundances, evolution and clustering, as well as nonlinear, nonlocal and stochastic halo bias, all of which matter for the next generation of large scale structure datasets. -
The World is Discrete
Olaf Dreyer Freelance Consultant
We argue that the scale-free spectrum that is observed in the cosmic microwave background is the result of a phase transition in the early universe. The observed tilt of the spectrum, which has been measured to be 0.04, is shown to be equal to the anomalous scaling dimension of the correlation function. The phase transition replaces inflation as the mechanism that produces this spectrum. The tilt further indicates that there is a fundamental small length scale in nature that we have not yet observed in any other way. -
Short Gamma-Ray Bursts and the Electromagnetic Counterparts of Gravitational Wave Sources
Edo Berger Harvard University
PIRSA:13090050Gamma-ray bursts are the most luminous and energetic explosions known in the universe. They appear in two varieties: long- and short-duration. The long GRB result from the core-collapse of massive stars, but until recently the origin of the short GRBs was shrouded in mystery. In this talk I will present several lines of evidence that point to the merger of compact objects binaries (NS-NS and/or NS-BH) as the progenitor systems of short GRBs. Within this framework, the observational data also allow us to independently determine the merger rate of these systems as input to the Advanced LIGO event rate, to infer the merger distribution timescale, and to determine the energy scale of the mergers. In addition, using radio to X-ray observations of short GRBs we can determine the expected electromagnetic properties of Advanced LIGO sources. -
Self-organized topological state with Majorana fermions
Marcel Franz University of British Columbia
Topological phases, quite generally, are difficult to come by. They either occur under rather extreme conditions (e.g. the quantum Hall liquids, which require high sample purity, strong magnetic fields and low temperatures) or demand fine tuning of system parameters, as in the majority of known topological insulators. Many perfectly sensible topological phases, such as the Weyl semimetals and topological superconductors, remain experimentally undiscovered. In this talk I will introduce a system in which a key dynamical parameter adjusts itself in response to the changing external conditions so that the ground state naturally favors the topological phase. The system consists of a quantum wire formed of individual magnetic atoms placed on the surface of an ordinary s-wave superconductor. It realizes the Kitaev paradigm of topological superconductivity when the wavevector characterizing the emergent spin helix dynamically self-tunes to support the topological phase. -
Coalgebras, Models and Logics for Quantum Systems
Coalgebras are a flexible tool commonly used in computer science to model abstract devices and systems. Coalgebraic models also come with a natural notion of logics for the systems being modelled. In this talk we will introduce coalgebras and aim to illustrate their usefulness for modelling physical systems. Extending earlier work of Abramsky, we will show how a weakening of the usual morphisms for coalgebras provides the flexibility to model quantum systems in an easy to motivate manner. We will then investigate how a natural extension to the usual notion of coalgebraic logic can be used to produce logics for reasoning about quantum systems and protocols. No prior knowledge of coalgebras will be assumed for this talk, and the emphasis throughout will be on examples rather than technical details. -
Orbifolds and topological defects
Daniel Plencner Ludwig-Maximilians-Universität München (LMU)
Orbifolding a 2-dimensional quantum field theory by a symmetry group admits an elegant description in terms of defect lines and their junction fields. This perspective offers a natural generalization of the concept of an orbifold, in which the role of the symmetry group is replaced by a defect with the structure of a (symmetric) separable Frobenius algebra. In this talk I will focus on the case of Landau-Ginzburg models, in which defects are described by matrix factorizations. After introducing the generalized twisted sectors and discussing topological bulk and boundary correlators in these sectors, I will present a simple proof of the Cardy condition and discuss some further consistency checks on the generalized orbifold theory. This talk is based on arXiv:1307.3141 with Ilka Brunner and Nils Carqueville. -
ΛCDM Large Scale Triumphs and Small Scale Challenges
Joel Primack University of California, Santa Cruz
ΛCDM has become the standard cosmological model because its predictions agree so well with observations of the cosmic microwave background and the large-scale structure of the universe. However ΛCDM has faced challenges on smaller scales. Some of these challenges, including the “angular momentum catastrophe" and the absence of density cusps in the centers of small galaxies, may be overcome with improvements in simulation resolution and feedback. Recent simulations appear to form realistic galaxies in agreement with observed scaling relations. Although dark matter halos start small and grow by accretion, the existence of a star-forming band of halo masses naturally explains why the most massive galaxies have the oldest stars, a phenomenon known as galactic “downsizing." The discovery of many faint galaxies in the Local Group is consistent with the large number of subhalos in ΛCDM simulations. There is increasing evidence for such substructure in galaxy dark matter halos from gaps in cold stellar streams in the Milky Way and Andromeda and from gravitational lensing flux anomalies, with the prospect of rapidly increasing data on that from ALMA. The “too big to fail" (TBTF) problem is the latest apparent challenge to ΛCDM. It arose from analysis of the Aquarius and Via Lactea very-high-resolution ΛCDM simulations of Milky-Way-mass dark matter halos. Each simulated halo has ∼10 subhalos so massive and dense that they would appear to be too big to fail to form lots of stars. The TBTF problem is that none of the observed dwarf satellite galaxies of the Milky Way or Andromeda have stars moving as fast as would be expected in these densest subhalos. This may indicate the need for a more complex theory of dark matter – but several recent papers have shown that subhalos in pure dark matter simulations like Aquarius or Via Lactea are significantly modified when baryonic effects are included, so as to solve the TBTF problem. Higher resolution simulations are needed to verify this.