Non-Abelian String and Particle Braiding in 3+1D Topological Order
Juven Wang Harvard University
PIRSA:14050015
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Renormalization Group Analysis of a Non-Fermi Liquid System
Ipsita Mandal Shiv Nadar University
PIRSA:14050014 -
Exotic Magnetism on the FCC Lattice of 5dn Double Perovskites
Edwin Kermarrec McMaster University
PIRSA:14050026 -
Entanglement, Ergodicity, and Many-Body Localization
Dmitry Abanin Princeton University
PIRSA:14050020 -
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Renormalization group approach to 3d group field theory
Sylvain Carrozza University of Burgundy
PIRSA:14040112 -
Renormalization of entanglement entropy and the gravitational effective action
Joshua Cooperman Radboud Universiteit Nijmegen
PIRSA:14040110 -
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The Asymptotic Safety Program: New results and an inconvenient truth
Martin Reuter Johannes Gutenberg University Mainz
PIRSA:14040108
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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. -
Exotic Magnetism on the FCC Lattice of 5dn Double Perovskites
Edwin Kermarrec McMaster University
PIRSA:14050026In the search for new exotic quantum states, the impact of strong spin-orbit interaction has been recently underlined with the discovery of the Jeff = ½ spin orbital Mott state in the 5d5 layered perovskites iridates [1]. The double perovskite structure, where the magnetic ions form a face-centered-cubic (fcc) sublattice, can accommodate a large variety of 5d transition metal elements, and therefore offers an ideal playground for systematic studies of the exotic magnetic and non-magnetic ground states stabilized by strong spin-orbit coupling [2]. Here, we report time-of-flight neutron scattering measurements on the antiferromagnetic, frustrated, cubic double perovskite system Ba2YOsO6. Its non-distorted fcc lattice is decorated with magnetic Os5+ (5d3) ions which undergo a magnetic transition to a long range ordered antiferromagnetic state below TN = 70 K, as revealed by magnetic Bragg peaks occuring at the [100] and [110] positions. Our inelastic data reveals a large spin gap to the spin-wave excitations Δ = 19(2) meV, unexpected for an orbitally quenched, d3 electronic configuration. We compare this result to the recent observation of a Δ=5 meV spin gap in the related cubic double perovskite Ba2YRuO6 (Ru5+, 4d3) [3], and conclude to a stronger spin-orbit coupling present in the heavier, 5d, osmate system.
[1] B. J. Kim et al., Science 323, 1329 (2009).
[2] G. Chen, R. Pereira and L. Balents, Phys. Rev. B 82, 174440 (2010);
G. Chen and L. Balents, Phys. Rev. B 84, 094420 (2011).
[3] J. P. Carlo et al., Phys. Rev. B 88, 024418 (2013). -
Entanglement, Ergodicity, and Many-Body Localization
Dmitry Abanin Princeton University
PIRSA:14050020We are used to describing systems of many particles by statistical mechanics. However, the basic postulate of statistical mechanics – ergodicity – breaks down in so-called many-body localized systems, where disorder prevents particle transport and thermalization. In this talk, I will present a theory of the many-body localized (MBL) phase, based on new insights from quantum entanglement. I will argue that, in contrast to ergodic systems, MBL eigenstates are not highly entangled. I will use this fact to show that MBL phase is characterized by an infinite number of emergent local conservation laws, in terms of which the Hamiltonian acquires a universal form. Turning to the experimental implications, I will describe the response of MBL systems to quenches: surprisingly, entanglement shows logarithmic in time growth, reminiscent of glasses, while local observables exhibit power-law approach to “equilibrium” values. I will support the presented theory with results of numerical experiments. I will close by discussing other directions in exploring ergodicity and its breaking in quantum many-body systems. -
Localization-Protected Quantum Order
David Huse Princeton University
PIRSA:14050013Systems that are many-body Anderson localized can exhibit symmetry-breaking long-range order or topological order in regimes where such order would be destroyed at equilibrium by thermal fluctuations. The ordering is dynamical: an ordered initial state stays ordered, being "protected" by the localization of all fluctuations. The simplest examples are quantum Ising models with static randomness. For the random quantum Ising chain this feature has been "known" but apparently not appreciated for close to half a century.
Ref.: Huse, et al., Phys. Rev. B 88, 014206 (2013). -
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Double scaling in tensor models
James Ryan Vinted (Germany)
PIRSA:14040114I present recent work on the double scaling limit of random tensor models through the analysis of their Schwinger-Dyson equations. This study exemplifies their potential for probing the continuum phase structure of these theories. -
Between Matrices and Tensors
Vincent Rivasseau University of Paris-Saclay
PIRSA:14040113Quartic tensor models can be rewritten in terms of intermediate matrix fields. The corresponding expansion is not only simpler, it suggests also new bridges between matrices, strings and tensors. -
Renormalization group approach to 3d group field theory
Sylvain Carrozza University of Burgundy
PIRSA:14040112I will start with a brief overview of tensorial group field theories with gauge invariant condition and their relation to spin foam models. The rest of the talk will be focused on the SU(2) theory in dimension 3, which is related to Euclidean 3d quantum gravity and has been proven renormalizable up to order 6 interactions. General renormalization group flow equations will be introduced, allowing in particular to understand the behavior of the relevant couplings in the neighborhood of the Gaussian fixed point. I will close with preliminary investigations about the existence of a non-trivial fixed point. -
Renormalization of entanglement entropy and the gravitational effective action
Joshua Cooperman Radboud Universiteit Nijmegen
PIRSA:14040110The entanglement entropy associated with a spatial boundary in quantum field theory is ultraviolet divergent, its leading term being proportional to the area of the boundary. Callan and Wilczek proposed a geometrical prescription for computing this entanglement entropy as the response of the gravitational effective action to a conically singular metric perturbation. I argue that the Callan-Wilczek prescription is rigorously justified at least for a particular class of quantum states each expressible as a Euclidean path integral. I then show that the entanglement entropy is rendered ultraviolet finite by precisely the counterterms required to cancel the ultraviolet divergences in the gravitational effective action. In particular, the leading contribution to the entanglement entropy is given by the renormalized Bekenstein-Hawking formula. These results apply to a general quantum field theory coupled to a fixed background metric, holding for arbitrary entangling surfaces with vanishing extrinsic curvature in any dimension, to all orders in perturbation theory in the quantum fields, and for all ultraviolet divergent terms in the entanglement entropy. I also reconcile these results on the entanglement entropy with the existing literature, compare them to the Wald entropy, and speculate on their interpretation and implication. -
Why matter matters in quantum gravity
Astrid Eichhorn Universität Heidelberg
PIRSA:14040109I will argue that a fundamental theory of quantum gravity that is applicable to our universe must include matter degrees of freedom. In my talk I will focus on the option that these are fundamental, in contrast to low-energy effective, degrees of freedom, and must thus be included in the microscopic dynamics of spacetime.
I will present evidence that dynamical Standard Model matter is compatible with asymptotically safe quantum gravity, while several "Beyond Standard Model" scenarios are disfavored. I will also discuss how the coupling to matter opens a window into the observational quantum gravity regime. -
The Asymptotic Safety Program: New results and an inconvenient truth
Martin Reuter Johannes Gutenberg University Mainz
PIRSA:14040108We briefly review the various components and their conceptual status of the full Asymptotic Safety Program which aims at finding a nonperturbative infinite-cutoff limit of a regularized functional integral for a quantum field theory of gravity. It is explained why in the continuum formulation based on the Effective Average Action the key requirement of background independence unavoidably results in a "bi-metric" framework, and recent results on truncated RG flows of bi-metric actions are presented. They suggest that the next generation of truncations that must be explored should be of bi-metric type. As an application, a method of characterizing and counting physical states is shown to arise.