A projection operator approach to the Bose-Hubbard model

We develop a projection operator formalism for studying both the zero temperature equilibrium phase diagram and the non-equilibrium dynamics of the Bose-Hubbard model. Our work, which constitutes an extension of Phys. Rev. Lett. {\bf 106}, 095702 (2011), shows that the method provides an accurate description of the equilibrium zero temperature phase diagram of the Bose-Hubbard model for several lattices in two- and three-dimensions (2D and 3D). We show that the accuracy of this method increases with the coordination number $z_0$ of the lattice and reaches to within 0.5% of quantum Monte Carlo data for lattices with $z_0=6$. We compute the excitation spectra of the bosons using this method in the Mott and the superfluid phases and compare our results with mean-field theory. We also show that the same method may be used to analyze the non-equilibrium dynamics of the model both in the Mott phase and near the superfluid-insulator quantum critical point where the hopping amplitude $J$ and the on-site interaction $U$ satisfy $z_0J/U \ll 1$. In particular, we study the non-equilibrium dynamics of the model both subsequent to a sudden quench of the hopping amplitude $J$ and during a ramp from $J_i$ to $J_f$ characterized by a ramp time $\tau$ and exponent $\alpha$: $J(t)=J_i +(J_f-J_i) (t/\tau)^{\alpha}$. We compute the wavefunction overlap $F$, the residual energy $Q$, the superfluid order parameter $\Delta(t)$, the equal-time order parameter correlation function $C(t)$, and the defect formation probability $P$ for the above-mentioned protocols and provide a comparison of our results to their mean-field counterparts. We find that $Q$, $F$, and $P$ do not exhibit the expected universal scaling. We explain this absence of universality and show that our results for linear ramps compare well with the recent experimental observations.Comment: v2; new references and new sections adde

Phenomenological Renormalization Group Methods

Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate critical behavior of the model on infinite lattice is obtained through the exact computation of some thermal quantities of the model on finite clusters. In this work some of these methods are reviewed, namely the mean field renormalization group, the effective field renormalization group and the finite size scaling renormalization group procedures. Although special emphasis is given to the mean field renormalization group (since it has been, up to now, much more applied an extended to study a wide variety of different systems) a discussion of their potentialities and interrelations to other methods is also addressed.Comment: Review Articl

Topological properties of the bond-modulated honeycomb lattice

We study the combined effects of lattice deformation, e-e interaction and spin-orbit coupling in a two-dimensional (2D) honeycomb lattice. We adopt different kinds of hopping modulation--generalized dimerization and a Kekule distortion--and calculate topological invariants for the non-interacting system and for the interacting system. We identify the parameter range (Hubbard U, hopping modulation, spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall Insulator.Comment: 8 pages, 4 figures: discussion improved, typos corrected, references updated. Matches version published in PR

Jets and outflows in Radio Galaxies: implications for AGN feedback

One of the main debated astrophysical problems is the role of the AGN feedback in galaxy formation. It is known that massive black holes have a profound effect on the formation and evolution of galaxies, but how black holes and galaxies communicate is still an unsolved problem. For Radio Galaxies, feedback studies have mainly focused on jet/cavity systems in the most massive and X-ray luminous galaxy clusters. The recent high-resolution detection of warm absorbers in some Broad Line Radio Galaxies allow us to investigate the interplay between the nuclear engine and the surrounding medium from a different perspective. We report on the detection of warm absorbers in two Broad Line Radio Galaxies, 3C 382 and 3C 390.3, and discuss the physical and energetic properties of the absorbing gas. Finally, we attempt a comparison between radio-loud and radio-quiet outflows.Comment: To be published in the proceedings of High Energy Phenomena in Relativistic Outflows III (HEPRO III, IJMPCS). 4 pages, 2 figure

Competing Glauber and Kawasaki Dynamics

Using a quantum formulation of the master equation we study a kinetic Ising model with competing stochastic processes: the Glauber dynamics with probability $p$ and the Kawasaki dynamics with probability $1 - p$. Introducing explicitely the coupling to a heat bath and the mutual static interaction of the spins the model can be traced back exactly to a Ginzburg Landau functional when the interaction is of long range order. The dependence of the correlation length on the temperature and on the probability $p$ is calculated. In case that the spins are subject to flip processes the correlation length disappears for each finite temperature. In the exchange dominated case the system is strongly correlated for each temperature.Comment: 9 pages, Revte

High-energy neutrinos from FR0 radio-galaxies?

The sources responsible for the emission of high-energy ($\gtrsim$ 100 TeV) neutrinos detected by IceCube are still unknown. Among the possible candidates, active galactic nuclei with relativistic jets are often examined, since the outflowing plasma seems to offer the ideal environment to accelerate the required parent high-energy cosmic rays. The non-detection of single point sources or -- almost equivalently -- the absence, in the IceCube events, of multiplets originating from the same sky position, constrains the cosmic density and the neutrino output of these sources, pointing to a numerous population of faint sources. Here we explore the possibility that FR0 radiogalaxies, the population of compact sources recently identified in large radio and optical surveys and representing the bulk of radio-loud AGN population, can represent suitable candidates for neutrino emission. Modeling the spectral energy distribution of a FR0 radiogalaxy recently associated to a $\gamma$-ray source detected by the Large Area Telescope onboard Fermi, we derive the physical parameters of its jet, in particular the power carried by it. We consider the possible mechanisms of neutrino production, concluding that $p\gamma$ reactions in the jet between protons and ambient radiation is too inefficient to sustain the required output. We propose an alternative scenario, in which protons, accelerated in the jet, escape from it and diffuse in the host galaxy, producing neutrinos as a result of $pp$ scattering with the interstellar gas, in strict analogy with the processes taking place in star-forming galaxies.Comment: 5 pages, 3 figures, accepted for publication in MNRA