Physics, Logic and Mathematics of Time
Louis Kauffman University of Illinois at Chicago
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Frozen Spin Ice Ground States in the Pyrochlore Magnet Tb2 Ti2 O7
Bruce Gaulin Canadian Association of Physicists
PIRSA:14050019 -
Measurements of Noice in Condensed Matter Systems Using Superconducting Qubits and Resonators
Adrian Lupascu Institute for Quantum Computing (IQC)
PIRSA:14050018 -
Strain Induces Helical Flat Band & Interface Superconductivity in Topological Crystalline Insulators
Evelyn Tang Rice University
PIRSA:14050017 -
Using β-NMR to Solve Hard Problems in Soft Condensed Matter
James Forrest University of Waterloo
PIRSA:14050023 -
Generic Spin Model for Honeycomb Iridates Beyond the Kitaev Limit
Jeffrey Rau University of Toronto
PIRSA:14050025 -
Fractionalized Charge Excitations in a Spin Liquid on Partially-Filled
Gang Chen Fudan University
PIRSA:14050024 -
Group Field Theory in dimension 4 - ε
Sylvain Carrozza University of Burgundy
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Experimental Sightings of the Quantum Spin Liquid
Young Lee Massachusetts Institute of Technology (MIT)
PIRSA:14050016 -
Geometric inequalities for black holes
Sergio Dain Universidad Nacional de Córdoba
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Non-Abelian String and Particle Braiding in 3+1D Topological Order
Juven Wang Harvard University
PIRSA:14050015 -
Renormalization Group Analysis of a Non-Fermi Liquid System
Ipsita Mandal Shiv Nadar University
PIRSA:14050014
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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. -
Group Field Theory in dimension 4 - ε
Sylvain Carrozza University of Burgundy
Rank 3 tensorial group fields theories with gauge invariance condition appear to be renormalizable on dimension 3 groups such as SU(2), but also on dimension 4 groups. Building on an analogy with ordinary scalar field theories, I will generalize such models to group dimension 4 - ε, and discuss what this might teach us about the physically relevant SU(2) case. -
Experimental Sightings of the Quantum Spin Liquid
Young Lee Massachusetts Institute of Technology (MIT)
PIRSA:14050016New states of matter may be produced if quantum effects and frustration conspire to prevent the ground state from achieving classical order. An example of a new quantum phase is the quantum spin liquid. Such spin liquids cannot be characterized by local order parameters; rather, they are distinctive by their possession of long range quantum entanglement. I will describe recent experimental progress in the quest to study quantum spin liquids in frustrated magnets. The kagome lattice, composed of corner-sharing triangles, is highly frustrated for antiferromagnetic spins. Materials based on the kagome lattice with spin-1/2 are ideal hosts for quantum spin liquid ground states. I will discuss our group’s work which includes single crystal growth, bulk characterization, and neutron scattering measurements of the S=1/2 kagome lattice material ZnCu3(OH)6Cl2 (also known as herbertsmithite). Our inelastic neutron scattering measurements of the spin correlations in a single crystal sample reveal that the excitations are fractionalized, a hallmark signature of spin liquid physics. -
Geometric inequalities for black holes
Sergio Dain Universidad Nacional de Córdoba
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole (angular momentum, charge, mass and horizon area) satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. Also, variants of these inequalities are valid for ordinary bodies. In this talk I will review recent results in this subject. -
Non-Abelian String and Particle Braiding in 3+1D Topological Order
Juven Wang Harvard University
PIRSA:14050015String and particle excitations are examined in a class of 3+1D topological order described by a discrete gauge theory with a gauge group G and a 4-cocycle twist ω4∈H4(G,R/Z) of G's cohomology group. We demonstrate the topological spin and the spin-statistics relation for the closed strings, and their multi-string braiding. The 3+1D twisted gauge theory can be characterized by a representation of SL(3,Z) modular transformation, which we find its generators Sxyz and Txy in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the 3D's direction z into a compact circle inserted with a gauge flux b, we can use the generators of SL(2,Z) subgroup of SL(3,Z), Sxy and Txy, to study the dimension reduction of the 3D topological order C3D to a direct sum of degenerate states of 2D topological orders C2Db in different fluxb sectors: C3D=⊕bC2Db. The 2D topological orders C2Db are described by 2D gauge theories of the group G twisted by the 3-cocycles ω3(b)dimensionally reduced from the 4-cocycle ω4. We show that the SL(2,Z) generators, Sxy and Txy, fully encodes a particular type of three-string braiding statistics for the connected sum of two Hopf links 221#221 configuration. With certain 4-cocycle twist, we find that, by threading a third string through two-string unlink 021 into three-string Hopf links 221#221 configuration, Abelian two-string statistics is promoted to non-Abelian three-string statistics. (Work done in arxiv.org/abs/1404.7854) -
Renormalization Group Analysis of a Non-Fermi Liquid System
Ipsita Mandal Shiv Nadar University
PIRSA:14050014We devise a renormalization group analysis for quantum field theories with Fermi surface to study scaling behaviour of non- Fermi liquid states in a controlled approximation. The non-Fermi liquid fixed points are identified from a Fermi surface in (m+1) spatial dimensions, while the co-dimension of Fermi surface is also extended to a generic value. We also study superconducting instability in such systems as a function of dimension and co-dimension of the Fermi surface. The key point in this whole analysis is that unlike in relativistic QFT, the Fermi momentum kF enters as a dimensionful parameter, thus modifying the naive scaling arguments. The effective coupling constant is found to be a combination of the original coupling constant and kF.