Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases

We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological (SPT) phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data is defined in terms of the statistics of bulk excitations, while the surface data is defined in terms of the statistics of surface excitations. An appealing property of this data is that it is plausibly complete in the sense that the bulk data uniquely distinguishes each 3D SPT phase, while the surface data uniquely distinguishes each gapped, symmetric surface. Our correspondence applies to any 3D bosonic SPT phase with finite Abelian unitary symmetry group. It applies to any surface that (1) supports only Abelian anyons and (2) has the property that the anyons are not permuted by the symmetries.Comment: 31 pages, 14 figures, 1 tabl

Modification of late time phase structure by quantum quenches

The consequences of the sudden change in the coupling constants (quenches) on the phase structure of the theory at late times are explored. We study in detail the three dimensional phi^6 model in the large N limit, and show that the phi^6 coupling enjoys a widened range of stability compared to the static scenario. Moreover, a new massive phase emerges, which for sufficiently large coupling becomes the dominant vacuum. We argue that these novel phenomena cannot be described by a simple thermalization effect or the emergence of a single effective temperature.Comment: 11 pages, 3 figure

Twist operators in higher dimensions

We study twist operators in higher dimensional CFT's. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in power series around n=1, with n being replica parameter. We show that the coefficients in this expansion are determined by higher point correlations of the energy-momentum tensor. In particular, the first and second terms, i.e. the first and second derivatives of the scaling dimension, have a simple universal form. We test these results using holography and free field theory computations, finding agreement in both cases. We also consider the `operator product expansion' of spherical twist operators and finally, we examine the behaviour of correlators of twist operators with other operators in the limit n ->1.Comment: 44 pages, 2 figure

Optimal Correlation Estimators for Quantized Signals

Using a maximum-likelihood criterion, we derive optimal correlation strategies for signals with and without digitization. We assume that the signals are drawn from zero-mean Gaussian distributions, as is expected in radio-astronomical applications, and we present correlation estimators both with and without a priori knowledge of the signal variances. We demonstrate that traditional estimators of correlation, which rely on averaging products, exhibit large and paradoxical noise when the correlation is strong. However, we also show that these estimators are fully optimal in the limit of vanishing correlation. We calculate the bias and noise in each of these estimators and discuss their suitability for implementation in modern digital correlators.Comment: 8 Pages, 3 Figures, Submitted to Ap

Holography in commercially available photoetchable glasses

Volume holographic gratings are recorded and retrieved in two commercially available glasses: Schott Foturan and Hoya PEG3. These materials are photoetchable, which describes their major application, but they also allow storage of volume holograms without any chemical etching. The samples are illuminated with ultraviolet light at a wavelength of 325 nm and thermally processed to achieve a maximum diffraction efficiency of approximately 9% for a 1-mm-thick sample. The two glasses show similar behavior; the diffraction efficiencies in Foturan tend to be slightly larger, whereas PEG3 tends to have weaker light scattering