Extended Variational Cluster Approximation

The variational cluster approximation (VCA) proposed by M. Potthoff {\it et al.} [Phys. Rev. Lett. {\bf 91}, 206402 (2003)] is extended to electron or spin systems with nonlocal interactions. By introducing more than one source field in the action and employing the Legendre transformation, we derive a generalized self-energy functional with stationary properties. Applying this functional to a proper reference system, we construct the extended VCA (EVCA). In the limit of continuous degrees of freedom for the reference system, EVCA can recover the cluster extension of the extended dynamical mean-field theory (EDMFT). For a system with correlated hopping, the EVCA recovers the cluster extension of the dynamical mean-field theory for correlated hopping. Using a discrete reference system composed of decoupled three-site single impurities, we test the theory for the extended Hubbard model. Quantitatively good results as compared with EDMFT are obtained. We also propose VCA (EVCA) based on clusters with periodic boundary conditions. It has the (extended) dynamical cluster approximation as the continuous limit. A number of related issues are discussed.Comment: 23 pages, 5 figures, statements about DCA corrected; published versio

The Dynamical Cluster Approximation (DCA) versus the Cellular Dynamical Mean Field Theory (CDMFT) in strongly correlated electrons systems

We are commenting on the article Phys. Rev. {\bf B 65}, 155112 (2002) by G. Biroli and G. Kotliar in which they make a comparison between two cluster techniques, the {\it Cellular Dynamical Mean Field Theory} (CDMFT) and the {\it Dynamical Cluster Approximation} (DCA). Based upon an incorrect implementation of the DCA technique in their work, they conclude that the CDMFT is a faster converging technique than the DCA. We present the correct DCA prescription for the particular model Hamiltonian studied in their article and conclude that the DCA, once implemented correctly, is a faster converging technique for the quantities averaged over the cluster. We also refer to their latest response to our comment where they argue that instead of averaging over the cluster, local observables should be calculated in the bulk of the cluster which indeed makes them converge much faster in the CDMFT than in the DCA. We however show that in their original work, the authors themselves use the cluster averaged quantities to draw their conclusions in favor of using the CDMFT over the DCA.Comment: Comment on Phys. Rev. B 65, 155112 (2002). 3 pages, 2 figure

Superconductivity in striped and multi-Fermi-surface Hubbard models: From the cuprates to the pnictides

Single- and multi-band Hubbard models have been found to describe many of the complex phenomena that are observed in the cuprate and iron-based high-temperature superconductors. Simulations of these models therefore provide an ideal framework to study and understand the superconducting properties of these systems and the mechanisms responsible for them. Here we review recent dynamic cluster quantum Monte Carlo simulations of these models, which provide an unbiased view of the leading correlations in the system. In particular, we discuss what these simulations tell us about superconductivity in the homogeneous 2D single-orbital Hubbard model, and how charge stripes affect this behavior. We then describe recent simulations of a bilayer Hubbard model, which provides a simple model to study the type and nature of pairing in systems with multiple Fermi surfaces such as the iron-based superconductors.Comment: Published as part of Superstripes 2011 (Rome) conference proceeding

Signatures of the A2A^2 term in ultrastrongly-coupled oscillators

We study a bosonic matter excitation coupled to a single-mode cavity field via electric dipole. Counter-rotating and $A^2$ terms are included in the interaction model, ${\mathbf A}$ being the vector potential of the cavity field. In the ultrastrong coupling regime the vacuum of the bare modes is no longer the ground state of the Hamiltonian and contains a nonzero population of polaritons, the true normal modes of the system. If the parameters of the model satisfy the Thomas-Reiche-Kuhn sum rule, we find that the two polaritons are always equally populated. We show how this prediction could be tested in a quenching experiment, by rapidly switching on the coupling and analyzing the radiation emitted by the cavity. A refinement of the model based on a microscopic minimal coupling Hamiltonian is also provided, and its consequences on our results are characterized analytically.Comment: 11 pages, 5 figure

Chains of large gaps between primes

Let $p_n$ denote the $n$-th prime, and for any $k \geq 1$ and sufficiently large $X$, define the quantity $$G_k(X) := \max_{p_{n+k} \leq X} \min( p_{n+1}-p_n, \dots, p_{n+k}-p_{n+k-1} ),$$ which measures the occurrence of chains of $k$ consecutive large gaps of primes. Recently, with Green and Konyagin, the authors showed that $$G_1(X) \gg \frac{\log X \log \log X\log\log\log\log X}{\log \log \log X}$$ for sufficiently large $X$. In this note, we combine the arguments in that paper with the Maier matrix method to show that $$G_k(X) \gg \frac{1}{k^2} \frac{\log X \log \log X\log\log\log\log X}{\log \log \log X}$$ for any fixed $k$ and sufficiently large $X$. The implied constant is effective and independent of $k$.Comment: 16 pages, no figure

Biaxial order parameter in the homologous series of orthogonal bent-core smectic liquid crystals

The fundamental parameter of the uniaxial liquid crystalline state that governs nearly all of its physical properties is the primary orientational order parameter (S) for the long axes of molecules with respect to the director. The biaxial liquid crystals (LCs) possess biaxial order parameters depending on the phase symmetry of the system. In this paper we show that in the first approximation a biaxial orthogonal smectic phase can be described by two primary order parameters: S for the long axes and C for the ordering of the short axes of molecules. The temperature dependencies of S and C are obtained by the Haller's extrapolation technique through measurements of the optical birefringence and biaxiality on a nontilted polar antiferroelectric (Sm-APA) phase of a homologous series of LCs built from the bent-core achiral molecules. For such a biaxial smectic phase both S and C, particularly the temperature dependency of the latter, are being experimentally determined. Results show that S in the orthogonal smectic phase composed of bent cores is higher than in Sm-A calamatic LCs and C is also significantly large

Tunable negative permeability in a quantum plasmonic metamaterial

We consider the integration of quantum emitters into a negative permeability metamaterial design in order to introduce tunability as well as nonlinear behavior. The unit cell of our metamaterial is a ring of metamolecules, each consisting of a metal nanoparticle and a two-level semiconductor quantum dot (QD). Without the QDs, the ring of the unit cell is known to act as an artificial optical magnetic resonator. By adding the QDs we show that a Fano interference profile is introduced into the magnetic field scattered from the ring. This induced interference is shown to cause an appreciable effect in the collective magnetic resonance of the unit cell. We find that the interference provides a means to tune the response of the negative permeability metamaterial. The exploitation of the QD's inherent nonlinearity is proposed to modulate the metamaterial's magnetic response with a separate control field.Comment: 11 pages, 6 figure

Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental Uncertainties

Recent theoretical and experimental improvements in the determination of charm and bottom quark masses are discussed. A new and improved evaluation of the contribution from the gluon condensate $$ to the charm mass determination and a detailed study of potential uncertainties in the continuum cross section for $b\bar b$ production is presented, together with a study of the parametric uncertainty from the $\alpha_s$-dependence of our results. The final results, $m_c(3 \text{GeV})=986(13)$MeV and $m_b(m_b)=4163(16)$MeV, represent, together with a closely related lattice determination $m_c(3\;{\rm GeV})=986(6)$MeV, the presently most precise determinations of these two fundamental Standard Model parameters. A critical analysis of the theoretical and experimental uncertainties is presented.Comment: 12 pages, presented at Quarks~2010, 16th International Seminar of High Energy Physics, Kolomna, Russia, June 6-12, 2010; v2: references adde