Non-Perturbative U(1) Gauge Theory at Finite Temperature

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_{\tau} N_s^3$ lattices for $N_{\tau}$ fixed by extrapolating spatial volumes of size $N_s\le 18$ to $N_s\to\infty$. Within the numerical accuracy of the thus obtained fits we find for $N_{\tau}=4$, 5 and~6 second order critical exponents, which exhibit no obvious $N_{\tau}$ dependence. The exponents are consistent with 3d Gaussian values, but not with either first order transitions or the universality class of the 3d XY model. As the 3d Gaussian fixed point is known to be unstable, the scenario of a yet unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.Comment: Extended version after referee reports. 6 pages, 6 figure

Renormalization of the periodic Anderson model: an alternative analytical approach to heavy Fermion behavior

In this paper a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians is applied to the periodic Anderson model (PAM) with the aim to describe heavy Fermion behavior. In this method high-energetic excitation operators instead of high energetic states are eliminated. We arrive at an effective Hamiltonian for a quasi-free system which consists of two non-interacting heavy-quasiparticle bands. The resulting renormalization equations for the parameters of the Hamiltonian are valid for large as well as small degeneracy $\nu_f$ of the angular momentum. An expansion in $1/\nu_f$ is avoided. Within an additional approximation which adapts the idea of a fixed renormalized \textit{f} level $\tilde{\epsilon}_{f}$, we obtain coupled equations for $\tilde{\epsilon}_{f}$ and the averaged \textit{f} occupation $$. These equations resemble to a certain extent those of the usual slave boson mean-field (SB) treatment. In particular, for large $\nu_f$ the results for the PRM and the SB approach agree perfectly whereas considerable differences are found for small $\nu_f$.Comment: 26 pages, 5 figures included, discussion of the DOS added in v2, accepted for publication in Phys. Rev.

Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.Comment: Final version as accepted for publication in Phys. Rev. B (4 pages, 3 figures

Wither the sliding Luttinger liquid phase in the planar pyrochlore

Using series expansion based on the flow equation method we study the zero temperature properties of the spin-1/2 planar pyrochlore antiferromagnet in the limit of strong diagonal coupling. Starting from the limit of decoupled crossed dimers we analyze the evolution of the ground state energy and the elementary triplet excitations in terms of two coupling constants describing the inter dimer exchange. In the limit of weakly coupled spin-1/2 chains we find that the fully frustrated inter chain coupling is critical, forcing a dimer phase which adiabatically connects to the state of isolated dimers. This result is consistent with findings by O. Starykh, A. Furusaki and L. Balents (Phys. Rev. B 72, 094416 (2005)) which is inconsistent with a two-dimensional sliding Luttinger liquid phase at finite inter chain coupling.Comment: 6 pages, 4 Postscript figures, 1 tabl

On the nature of the FBS blue stellar objects and the completeness of the Bright Quasar Survey. II

In Paper I (Mickaelian et al. 1999), we compared the surface density of QSOs in the Bright Quasar Survey (BQS) and in the First Byurakan Survey (FBS) and concluded that the completeness of the BQS is of the order of 70% rather than 30-50% as suggested by several authors. A number of new observations recently became available, allowing a re-evaluation of this completeness. We now obtain a surface density of QSOs brighter than B = 16.16 in a subarea of the FBS covering ~2250 deg^2, equal to 0.012 deg^-2 (26 QSOs), implying a completeness of 53+/-10%.Comment: LaTeX 2e, 11 pages, 3 tables and 3 figures (included in text). To appear in Astrophysics. Uses a modified aaspp4.sty (my_aaspp4.sty), included in packag

H\"older equicontinuity of the integrated density of states at weak disorder

H\"older continuity, $|N_\lambda(E)-N_\lambda(E')|\le C |E-E'|^\alpha$, with a constant $C$ independent of the disorder strength $\lambda$ is proved for the integrated density of states $N_\lambda(E)$ associated to a discrete random operator $H = H_o + \lambda V$ consisting of a translation invariant hopping matrix $H_o$ and i.i.d. single site potentials $V$ with an absolutely continuous distribution, under a regularity assumption for the hopping term.Comment: 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4 combine

Critical wave-packet dynamics in the power-law bond disordered Anderson Model

We investigate the wave-packet dynamics of the power-law bond disordered one-dimensional Anderson model with hopping amplitudes decreasing as $H_{nm}\propto |n-m|^{-\alpha}$. We consider the critical case ($\alpha=1$). Using an exact diagonalization scheme on finite chains, we compute the participation moments of all stationary energy eigenstates as well as the spreading of an initially localized wave-packet. The eigenstates multifractality is characterized by the set of fractal dimensions of the participation moments. The wave-packet shows a diffusive-like spread developing a power-law tail and achieves a stationary non-uniform profile after reflecting at the chain boundaries. As a consequence, the time-dependent participation moments exhibit two distinct scaling regimes. We formulate a finite-size scaling hypothesis for the participation moments relating their scaling exponents to the ones governing the return probability and wave-function power-law decays