Renormalization Group Study of the Electron-phonon Interaction in the High Tc Cuprates

We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.Comment: 4 pages, 3 figures, references added, added more details about others' previous studie

Phase properties of hypergeometric states and negative hypergeometric states

We show that the three quantum states (P$\acute{o}$lya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediates states which interpolate between the binomial states and negative binomial states are essentially identical. By using the Hermitial-phase-operator formalism, the phase properties of the hypergeometric states and negative hypergeometric states are studied in detail. We find that the number of peaks of phase probability distribution is one for the hypergeometric states and $M$ for the negative hypergeometric states.Comment: 7 pages, 4 figure

Evidence from the Very Long Baseline Array that J1502SE/SW are Double Hotspots, not a Supermassive Binary Black Hole

SDSS J150243.09+111557.3 is a merging system at z = 0.39 that hosts two confirmed AGN, one unobscured and one dust-obscured, offset by several kiloparsecs. Deane et al. recently reported evidence from the European VLBI Network (EVN) that the dust-obscured AGN exhibits two flat-spectrum radio sources, J1502SE/SW, offset by 26 mas (140 pc), with each source being energized by its own supermassive black hole (BH). This intriguing interpretation of a close binary BH was reached after ruling out a double-hotspot scenario, wherein both hotspots are energized by a single, central BH, a configuration occuring in the well-studied Compact Symmetric Objects. When observed with sufficient sensitivity and resolution, an object with double hotspots should have an edge-brightened structure. We report evidence from the Very Long Baseline Array (VLBA) for just such a structure in an image of the obscured AGN with higher sensitivity and resolution than the EVN images. We thus conclude that a double-hotspot scenario should be reconsidered as a viable interpretation for J1502SE/SW, and suggest further VLBA tests of that scenario. A double-hotspot scenario could have broad implications for feedback in obscured AGNs. We also report a VLBA detection of high-brightness-temperature emssion from the unobscured AGN that is offset several kiloparsecs from J1502SE/SW.Comment: 12 pages, 1 figure, accepted by ApJL on 2014 July 2