6,526 research outputs found

    Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization

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    We introduce normal coordinates on the infinite dimensional group GG introduced by Connes and Kreimer in their analysis of the Hopf algebra of rooted trees. We study the primitive elements of the algebra and show that they are generated by a simple application of the inverse Poincar\'e lemma, given a closed left invariant 1-form on GG. For the special case of the ladder primitives, we find a second description that relates them to the Hopf algebra of functionals on power series with the usual product. Either approach shows that the ladder primitives are given by the Schur polynomials. The relevance of the lower central series of the dual Lie algebra in the process of renormalization is also discussed, leading to a natural concept of kk-primitiveness, which is shown to be equivalent to the one already in the literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy

    Probing many-body localization in a disordered quantum magnet

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    Quantum states cohere and interfere. Quantum systems composed of many atoms arranged imperfectly rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent clusters of spins by driving the system beyond its linear response regime at a single frequency and measuring the resulting "hole" in the overall linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the disordered Ising magnet, LiHo0.045Y0.955F4\mathrm{LiHo_{0.045}Y_{0.955}F_4}, the quality factor QQ for spectral holes can be as high as 100,000. We tune the dynamics of the quantum degrees of freedom by sweeping the Fano mixing parameter qq through zero via the amplitude of the ac pump as well as a static external transverse field. The zero-crossing of qq is associated with a dissipationless response at the drive frequency, implying that the off-diagonal matrix element for the two-level system also undergoes a zero-crossing. The identification of localized two-level systems in a dense and disordered dipolar-coupled spin system represents a solid state implementation of many-body localization, pushing the search forward for qubits emerging from strongly-interacting, disordered, many-body systems.Comment: 22 pages, 6 figure

    Interplay of disorder and geometrical frustration in doped Gadolinium Gallium Garnet

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    The geometrically-frustrated, triangular antiferromagnet GGG exhibits a rich mix of short-range order and isolated quantum states. We investigate the effects of up to 1% Neodymium substitution for Gallium on the ac magnetic response at temperatures below 1 K in both the linear and nonlinear regimes. Substitutional disorder actually drives the system towards a more perfectly frustrated state, apparently compensating for the effect of imperfect Gadolinium/Gallium stoichiometry, while at the same time more closely demarcating the boundaries of isolated, coherent clusters composed of hundreds of spins. Optical measurements of the local Nd environment substantiate the picture of an increased frustration index with doping.Comment: 5 pages, 5 figure

    Quantum and Classical Glass Transitions in LiHoxY1xF4Li Ho_x Y_{1-x} F_4

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    When performed in the proper low field, low frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in transverse field, LiHoxY1xF4\text{LiHo}_x\text{Y}_{1-x}\text{F}_4, prove the existence of a spin glass transition for xx = 0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields.Comment: 5 pages, 5 figures. Updated figure 3 with corrected calibration information for thermometr

    Continuous and Discontinuous Quantum Phase Transitions in a Model Two-Dimensional Magnet

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    The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a 2-dimensional square lattice, is simple and soluble, but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry-Sutherland material, SrCu2(BO3)2, in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution x-ray measurements exploit what emerges as a remarkably strong spin-lattice coupling to both monitor the magnetic behavior and the absence or presence of structural discontinuities. In the low-pressure spin-singlet regime, the onset of magnetism results in an expansion of the lattice with decreasing temperature, which permits a determination of the pressure dependent energy gap and the almost isotropic spin-lattice coupling energies. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure.Comment: 16 pages, 4 figures. Accepted for publication in PNA

    Strange Quarks Nuggets in Space: Charges in Seven Settings

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    We have computed the charge that develops on an SQN in space as a result of balance between the rates of ionization by ambient gammas and capture of ambient electrons. We have also computed the times for achieving that equilibrium and binding energy of the least bound SQN electrons. We have done this for seven different settings. We sketch the calculations here and give their results in the Figure and Table II; details are in the Physical Review D.79.023513 (2009).Comment: Six pages, one figure. To appear in proceedings of the 2008 UCLA coference on dark matter and dark energ

    Quantum Barkhausen Noise Induced by Domain Wall Co-Tunneling

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    Most macroscopic magnetic phenomena (including magnetic hysteresis) are typically understood classically. Here, we examine the dynamics of a uniaxial rare-earth ferromagnet deep within the quantum regime, so that domain wall motion, and the associated hysteresis, is dominated by large-scale quantum tunneling of spins, rather than classical thermal activation over a potential barrier. The domain wall motion is found to exhibit avalanche dynamics, observable as an unusual form of Barkhausen noise. We observe non-critical behavior in the avalanche dynamics that only can be explained by going beyond traditional renormalization group methods or classical domain wall models. We find that this ``quantum Barkhausen noise'' exhibits two distinct mechanisms for domain wall movement, each of which is quantum-mechanical, but with very different dependences on an external magnetic field applied transverse to the spin (Ising) axis. These observations can be understood in terms of the correlated motion of pairs of domain walls, nucleated by co-tunneling of plaquettes (sections of domain wall), with plaquette pairs correlated by dipolar interactions; this correlation is suppressed by the transverse field. Similar macroscopic correlations may be expected to appear in the hysteresis of other systems with long-range interactions.Comment: 11 pages, 4 figure

    Inference with interference between units in an fMRI experiment of motor inhibition

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    An experimental unit is an opportunity to randomly apply or withhold a treatment. There is interference between units if the application of the treatment to one unit may also affect other units. In cognitive neuroscience, a common form of experiment presents a sequence of stimuli or requests for cognitive activity at random to each experimental subject and measures biological aspects of brain activity that follow these requests. Each subject is then many experimental units, and interference between units within an experimental subject is likely, in part because the stimuli follow one another quickly and in part because human subjects learn or become experienced or primed or bored as the experiment proceeds. We use a recent fMRI experiment concerned with the inhibition of motor activity to illustrate and further develop recently proposed methodology for inference in the presence of interference. A simulation evaluates the power of competing procedures.Comment: Published by Journal of the American Statistical Association at http://www.tandfonline.com/doi/full/10.1080/01621459.2012.655954 . R package cin (Causal Inference for Neuroscience) implementing the proposed method is freely available on CRAN at https://CRAN.R-project.org/package=ci
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