Universality of the single-particle spectra of cuprate superconductors

All the available data for the dispersion and linewidth of the single-particle spectra above the superconducting gap and the pseudogap in metallic cuprates for any doping has universal features. The linewidth is linear in energy below a scale $\omega_c$ and constant above. The cusp in the linewidth at $\omega_c$ mandates, due to causality, a "waterfall", i.e., a vertical feature in the dispersion. These features are predicted by a recent microscopic theory. We find that all data can be quantitatively fitted by the theory with a coupling constant $\lambda_0$ and an upper cutoff at $\omega_c$ which vary by less than 50% among the different cuprates and for varying dopings. The microscopic theory also gives these values to within factors of O(2).Comment: 4 pages, 4 figures; accepted by Phys. Rev. Let

Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties

The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets representing local averages and local differences. Although one-to-one transformations of data sets are possible, the advantage of the wavelet transform is as an approximation scheme for the efficient calculation of thermodynamic and ensemble properties. Even under the most drastic of approximations, the resulting errors in the values obtained for average absolute magnetization, free energy, and heat capacity are on the order of 10%, with a corresponding computational efficiency gain of two orders of magnitude for a system such as a $4\times 4$ Ising lattice. In addition, the errors in the results tend toward zero in the neighborhood of fixed points, as determined by renormalization group theory.Comment: 13 pages plus 7 figures (PNG

Entanglement renormalization and gauge symmetry

A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints, and can be regarded as the low energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low energy, effective descriptions of lattice models with a local symmetry, such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure, and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of the toric code with a magnetic field, equivalent to Z2 lattice gauge theory, for lattices with up to 16 x 16 sites (16^2 x 2 = 512 spins) on a torus. We reproduce the well-known ground state phase diagram of the model, consisting of a deconfined and spin polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground state fidelities, Wilson loops, and several other quantities.Comment: reviewed version as published in PRB; this version includes a new section about the accuracy of the results several corrections and added citation

Homogeneous versus Spiral Phases of Hole-doped Antiferromagnets: A Systematic Effective Field Theory Investigation

Using the low-energy effective field theory for magnons and holes -- the condensed matter analog of baryon chiral perturbation theory for pions and nucleons in QCD -- we study different phases of doped antiferromagnets. We systematically investigate configurations of the staggered magnetization that provide a constant background field for doped holes. The most general configuration of this type is either constant itself or it represents a spiral in the staggered magnetization. Depending on the values of the low-energy parameters, a homogeneous phase, a spiral phase, or an inhomogeneous phase is energetically favored. The reduction of the staggered magnetization upon doping is also investigated.Comment: 35 pages, 5 figure

Relevance of multiband Jahn-Teller effects on the electron-phonon interaction in A3A_3C60_{60}

Assessing the effective relevance of multiband effects in the fullerides is of fundamental importance to understand the complex superconducting and transport properties of these compounds. In this paper we investigate in particular the role of the multiband effects on the electron-phonon (el-ph) properties of the $t_{1u}$ bands coupled with the Jahn-Teller intra-molecular $H_g$ vibrational modes in the C$_{60}$ compounds. We show that, assuming perfect degeneracy of the electronic bands, vertex diagrams arising from the breakdown of the adiabatic hypothesis, are one order of magnitude smaller than the non-crossing terms usually retained in the Migdal-Eliashberg (ME) theory. These results permit to understand the robustness on ME theory found by numerical calculations. The effects of the non degeneracy of the $t_{1u}$ in realistic systems are also analyzed. Using a tight-binding model we show that the el-ph interaction is mainly dominated by interband scattering within a single electronic band. Our results question the reliability of a degenerate band modeling and show the importance of these combined effects in the $A_3$C$_{60}$ family.Comment: 5 pages, 3 eps figure

Dualities in Spin Ladders

We introduce a set of discrete modular transformations $T_\ell,U_\ell$ and $S_\ell$ in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the 2 legged ladder we show that the $RVB$ phase is invariant under the $S_\ell$ transformation, while the Haldane phase is invariant under $U_\ell$. These two phases are related by $T_\ell$. Moreover there is a "mixed" phase, that is invariant under $T_\ell$, and which under $U_\ell$ becomes the RVB phase, while under $S_\ell$ becomes the Haldane phase. For odd ladders there exists only the $T_\ell$ transformation which, for strong coupling, maps the effective antiferromagnetic spin 1/2 chain into the spin 3/2 chain.Comment: REVTEX file, 5 pages, 2 EPS figure

Extended Defects in the Potts-Percolation Model of a Solid: Renormalization Group and Monte Carlo Analysis

We extend the model of a 2$d$ solid to include a line of defects. Neighboring atoms on the defect line are connected by ?springs? of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the 3- and 4-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.Comment: 13 figures, 17 page

Slave-boson approach to the infinite-U Anderson-Holstein impurity model

The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on the interplay between the strong electron correlation and the weak electron-phonon interaction. The slave boson method has been employed in combination with the large degeneracy expansion (1/N) technique. The charge and spin susceptibilities and the phonon propagator are obtained in the approximation scheme where the saddle point configuration and the Gaussian 1/N fluctuations are taken into account. The spin susceptibility is found not to be renormalized by electron-phonon interaction, while the charge susceptibility is renormalized. From the renormalized charge susceptibility the Kondo temperature is found to increase by the electron-phonon interaction. It turns out that the bosonic 1/N Gaussian fluctuations play a very crucial role, in particular, for the phonon propagator.Comment: 12pages, 3 figures. Published in Physical Review

Anomalous impurity effects in nonadiabatic superconductors

We show that, in contrast with the usual electron-phonon Migdal-Eliashberg theory, the critical temperature Tc of an isotropic s-wave nonadiabatic superconductor is strongly reduced by the presence of diluted non-magnetic impurities. Our results suggest that the recently observed Tc-suppression driven by disorder in K3C60 [Phys. Rev. B vol.55, 3866 (1997)] and in Nd(2-x)CexCuO(4-delta) [Phys. Rev. B vol.58, 8800 (1998)] could be explained in terms of a nonadiabatic electron-phonon coupling. Moreover, we predict that the isotope effect on Tc has an impurity dependence qualitatively different from the one expected for anisotropic superconductors.Comment: 10 pages, euromacr.tex, europhys.sty, 6 figures. Replaced with accepted version (Europhysics Letters

Unitary Chern-Simons matrix model and the Villain lattice action

We use the Villain approximation to show that the Gross-Witten model, in the weak- and strong-coupling limits, is related to the unitary matrix model that describes U(N) Chern-Simons theory on S^3. The weak-coupling limit corresponds to the q->1 limit of the Chern-Simons theory while the strong-coupling regime is related to the q->0 limit. In the latter case, there is a logarithmic relationship between the respective coupling constants. We also show how the Chern-Simons matrix model arises by considering two-dimensional Yang-Mills theory with the Villain action. This leads to a U(1)^N theory which is the Abelianization of 2d Yang-Mills theory with the heat-kernel lattice action. In addition, we show that the character expansion of the Villain lattice action gives the q deformation of the heat kernel as it appears in q-deformed 2d Yang-Mills theory. We also study the relationship between the unitary and Hermitian Chern-Simons matrix models and the rotation of the integration contour in the corresponding integrals.Comment: 17 pages, Minor corrections to match the published versio