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Anomalies of discrete symmetries and Symmetry Protected Topological Phases
Anton Kapustin California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
Noncommutative geometry and the symmetries of the standard model
Fedele Lizzi University of Naples Federico II
The Case for an Alternative Cosmology
Jayant Narlikar IUCAA - The Inter-University Centre for Astronomy and Astrophysics
John Paul Robinson: Art, Science and Myth
PIRSA:14050062Physics, Logic and Mathematics of Time
Louis Kauffman University of Illinois at Chicago
Frozen Spin Ice Ground States in the Pyrochlore Magnet Tb2 Ti2 O7
Bruce Gaulin Canadian Association of Physicists
PIRSA:14050019Measurements of Noice in Condensed Matter Systems Using Superconducting Qubits and Resonators
Adrian Lupascu Institute for Quantum Computing (IQC)
PIRSA:14050018Strain Induces Helical Flat Band & Interface Superconductivity in Topological Crystalline Insulators
Evelyn Tang Rice University
PIRSA:14050017Using β-NMR to Solve Hard Problems in Soft Condensed Matter
James Forrest University of Waterloo
PIRSA:14050023Generic Spin Model for Honeycomb Iridates Beyond the Kitaev Limit
Jeffrey Rau University of Toronto
PIRSA:14050025Fractionalized Charge Excitations in a Spin Liquid on Partially-Filled
Gang Chen Fudan University
PIRSA:14050024
Scattering of emerging excitations in Matrix Product States
Jutho Haegeman Ghent University
We review the formalism of matrix product states and one of its recent generalisations which allows to variationally determine the dispersion relation of elementary excitations in generic one-dimensional quantum spin chains. These elementary excitations dominate the low energy effective behaviour of the system. We discuss recent work where we show how we can also describe the effective interaction between these excitations – as mediated by the strongly correlated ground state – and how we can extract the corresponding S matrix. With these two ingredients, we can already build a highly non-trivial low-energy description of any microscopic Hamiltonian by assuming that higher order scattering processes are negligible. This allows to extract accurate information about the behaviour of the system under perturbations or at finite temperature, as we illustrate using the spin 1 Heisenberg model.Anomalies of discrete symmetries and Symmetry Protected Topological Phases
Anton Kapustin California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
There is a close connection between Symmetry Protected Topological Phases and anomalies: a surface of an SPT phase typically has a global symmetry with a nonvanishing 't Hooft anomaly which is canceled by the anomaly inflow from the bulk. This observation together with the known results about the classification of SPT phases suggest that anomalies are much more ubiquitous than thought previously and do not require chiral fermions We elucidate the physical mechanism of anomalies and give examples of bosonic theories with 't Hooft anomalies in various dimensions.Noncommutative geometry and the symmetries of the standard model
Fedele Lizzi University of Naples Federico II
I will describe Connes approach to the standard model based on spectral noncommutative geometry with particular emphasis on the symmetries. The model poses constraints which are satisfied by the standard model group, and does not leave much room for other possibilities. There is however a possibility for a larger symmetry (the ``grand algebra'') which may also be instrumental to obtain the correct mass of the Higgs.The Case for an Alternative Cosmology
Jayant Narlikar IUCAA - The Inter-University Centre for Astronomy and Astrophysics
This talk will describe the Quasi-Steady State Cosmology proposed in 1993 by Fred Hoyle, Geoffrey Burbidge and Jayant Narlikar. Starting with the motivation for this exercise, a formal field theoretic framework inspired by Mach’s principle is shown to lead to this model. The model is a generalization of the classical steady state model in the sense that it is driven by a scalar field which causes creation in explosive form. Such ‘minicreation events’ lead to a universe with a long term de Sitter expansion superposed with oscillations of shorter time scales. It is shown that this cosmology explains all the observed cosmological features and that there exist potential tests to distinguish between this cosmology and the standard big bang cosmology.John Paul Robinson: Art, Science and Myth
PIRSA:14050062Canadian glass artist and Renaissance man, John Paul Robinson, explores the mythic potential of science. Explaining that, “This is the idea that scientific discovery is changing our mythology by changing our understanding of the world and our place in it.” Backed with a firm understanding of the science he references, his sculptures poetically interpret such theoretical phenomena as wave particles, string mathematics and black holes. Most people, especially scientists see mythology and science as mutually exclusive and many believe that a scientific understanding of the world will eventually eliminate the need for myth. This idea is based on a misunderstanding as to what myth really is and it’s relationship to science. Myth is not superstition, fairy tail or lies nor is it truth, history or fact. Myth is Art. Myth is a picture, a story, a map; we use to navigate the world. Not the external material world but the world we all create and hold in our minds. In every human mind is a mythic picture of the world that provides the stage for all we experience. This picture not only helps us navigate our world but also performs the critical function of informing our sense of place and belonging within that world. Science cannot replace myth but it can inform it for mythology deals not with the mysteries generated by our ignorance of how the world works but by our understanding of how the world works. The mathematics of string theory is a powerful tool to describe the world but even physicists have to close their eyes and picture in their minds the world their equations are describing. The equation is pure logic and reason, but the picture of tiny strings playing the music that creates the universe is pure mythology. Award-winning glass artist and instructor John Paul Robinson was educated at the Georgian College of Arts and Technology in Barrie, Ontario, and the Ontario College of Art, where he subsequently taught for a number of years. His work has been exhibited in solo shows throughout Canada and the United States, in cities such as Montreal, Toronto and Chicago. Robinson’s works are held in the collections of The Museum of Civilization in Ottawa, Ontario, the Museum of American Glass in Millville, New Jersey and the Musée des Beaux-arts de Montréal, Québec. He has also created the Amber Archive, an annual participatory art project to communicate our existence and creative endeavours (by artists, designers and scientists) to beings millions of years in the future.Physics, Logic and Mathematics of Time
Louis Kauffman University of Illinois at Chicago
Consider discrete physics with a minimal time step taken to be
tau. A time series of positions q,q',q'', ... has two classical
observables: position (q) and velocity (q'-q)/tau. They do not commute,
for observing position does not force the clock to tick, but observing
velocity does force the clock to tick. Thus if VQ denotes first observe
position, then observe velocity and QV denotes first observe velocity,
then observe position, we have
VQ: (q'-q)q/tau
QV: q'(q'-q)/tau
(since after one tick the position has moved from q to q').
Thus [Q,V]= QV - VQ = (q'-q)^2/tau. If we consider the equation
[Q,V] = k (a constant), then k = (q'-q))^2/tau and this is recognizably
the diffusion constant that arises in a process of Brownian motion.
Thus, starting with the simplest assumptions for discrete physics, we are
lead to recognizable physics. We take this point of view and follow it
in both physical and mathematical directions. A first mathematical
direction is to see how i, the square root of negative unity, is related
to the simplest time series: ..., -1,+1,-1,+1,... and making the
above analysis of time series more algebraic leads to the following
interpetation for i. Let e=[-1,+1] and e'=[+1,-1] denote, as ordered
pairs, two phase-shifted versions of the alternating series above.
Define an operator b such that eb = be' and b^2 = 1. Regard b as a time
shifting operator. The operator b shifts the alternating series by one
half its period. Regard e' = -e and ee' = [-1.-1] = -1 (combining term by
term). Then let i = eb. We have ii = (eb)(eb) = ebeb = ee'bb = -1. Thus ii = -1
through the definition of i as eb, a temporally sensitive entity that
shifts it phase in the course of interacting with (a copy of) itself.
By going to i as a discrete dynamical system, we can come back to the
general features of discrete dynamical systems and look in a new way at
the role of i in quantum mechanics. Note that the i we have constructed is
already part of a simple Clifford algebra generated by e and b with
ee = bb = 1 and eb + be = 0. We will discuss other mathematical physical
structures such as the Schrodinger equation, the Dirac equation and the
relationship of a simple logical operator (generalizing negation) with
Majorana Fermions.Frozen Spin Ice Ground States in the Pyrochlore Magnet Tb2 Ti2 O7
Bruce Gaulin Canadian Association of Physicists
PIRSA:14050019Tb2Ti2O7 was one of the first pyrochlore magnets to be studied as a candidate for a spin liquid or cooperative paramagnet, and its ground state has remained enigmatic for fifteen years. Recent time-of-flight neutron scattering studies have shown that it enters a glassy Spin Ice ground state, characterized by frozen short range order over about 8 conventional unit cells, and the formation of a ~ 0.08 meV gap in its spin excitation spectrum at the appropriate quasi-Bragg wave vectors. I will introduce the relevant Spin Ice physics background, and describe how the experiments are performed. The new H-T phase diagram for Tb2Ti2O7 in a [110] magnetic field will be presented. This shows that its frozen (i.e. glassy) Spin Ice ground state (at low temperature and zero field) and its conventional field-induced ordered phase (at low temperature and high fields) bracket the cooperative paramagnetic phase which generated the original interest in this fascinating magnet.Measurements of Noice in Condensed Matter Systems Using Superconducting Qubits and Resonators
Adrian Lupascu Institute for Quantum Computing (IQC)
PIRSA:14050018Superconducting qubits based on Josephson junctions and resonators are presently leading candidates for the implementation of quantum computing. These systems couple strongly to their environment, which often makes preservation of coherence challenging. This strong coupling can be turned into an advantage: it enables the investigation of noise and loss at low temperatures. I will discuss two topics. The first topic is the use of superconducting flux qubits to measure magnetic flux noise. The second topic is the measurement of microwave loss in amorphous dielectric materials. Experiments with superconducting coherent systems can be used to extract new information on flux noise and dielectric loss, not accessible using other methods used in the past, providing useful input to theoretical developments.Strain Induces Helical Flat Band & Interface Superconductivity in Topological Crystalline Insulators
Evelyn Tang Rice University
PIRSA:14050017Topological crystalline insulators in IV-VI compounds host novel topological surface states, that at low energy, consist of multi-valley massless Dirac fermions. We show that strain generically acts as an effective gauge field on these Dirac fermion surface states and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict this is naturally realized in IV-VI semiconductor heterostructures due to the spontaneous formation of a misfit dislocation array at the interface, where the zero-energy Landau orbitals form a nearly flat band. We propose that the high density of states of this topological flat band gives rise to the experimentally observed interface superconductivity in IV-VI semiconductor multilayers at temperatures that are unusually high for semiconductors, and explains its non-BCS dependence on dislocation array period.Using β-NMR to Solve Hard Problems in Soft Condensed Matter
James Forrest University of Waterloo
PIRSA:14050023Beta-detected nuclear spin relaxation of 8Li+ has been used to study important problems in polymer physics. In the first case we probe the depth dependence of molecular dynamics in high- and low-molecular-weight deuterated polystyrene (PS-d8). The average nuclear spin-lattice relaxation rate, 1/T1 avg, is a measure of the spectral density of the polymer dynamics at the Larmor frequency (41MHz at 6.55Tesla). The mean fluctuation rate decreases approximately exponentially with distance from the free surface, returning to bulk behavior for depths greater than ~10nm and the effective thickness of the surface region increases with increasing temperature. These results present challenges for the current understanding of dynamics near the free surface of polymer glasses. In the second case, we use the technique to make the first quantitative measurements of surface segregation in samples that are blends of two chemically identical polymers with different degrees of polymerization.Generic Spin Model for Honeycomb Iridates Beyond the Kitaev Limit
Jeffrey Rau University of Toronto
PIRSA:14050025Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the J=1/2 Mott insulator in these materials exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here we provide the generic nearest-neighbour spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120 degree and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.Fractionalized Charge Excitations in a Spin Liquid on Partially-Filled
Gang Chen Fudan University
PIRSA:14050024Electron charge may fractionalize in a quantum spin liquid Mott insulator. We study the Mott transition from a metal to a cluster Mott insulator in the 1/4- and 1/8-filled pyrochlore lattice systems. Such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsion. The resulting cluster Mott insulator is a quantum spin liquid with spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in X-ray scattering experiments. This and other experimental signatures of the quantum spin and fractionalized charge liquid state are discussed in light of candidate materials with partially-filled bands on pyrochlore lattices. “Fractionalized Charge Excitations in a Spin Liquid on Partially-Filled Pyrochlore Lattice” Electron charge may fractionalize in a quantum spin liquid Mott insulator. We study the Mott transition from a metal to a cluster Mott insulator in the 1/4- and 1/8-filled pyrochlore lattice systems. Such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsion. The resulting cluster Mott insulator is a quantum spin liquid with spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in X-ray scattering experiments. This and other experimental signatures of the quantum spin and fractionalized charge liquid state are discussed in light of candidate materials with partially-filled bands on pyrochlore lattices.