A Compact Approximate Solution to the Friedel-Anderson Impuriy Problem

An approximate groundstate of the Anderson-Friedel impurity problem is presented in a very compact form. It requires solely the optimization of two localized electron states and consists of four Slater states (Slater determinants). The resulting singlet ground state energy lies far below the Anderson mean field solution and agrees well with the numerical results by Gunnarsson and Schoenhammer, who used an extensive 1/N_{f}-expansion for a spin 1/2 impurity with double occupancy of the impurity level. PACS: 85.20.Hr, 72.15.R

Theory of Core-Level Photoemission and the X-ray Edge Singularity Across the Mott Transition

The zero temperature core-level photoemission spectrum is studied across the metal to Mott insulator transition using dynamical mean-field theory and Wilson's numerical renormalization group. An asymmetric power-law divergence is obtained in the metallic phase with an exponent alpha(U,Q)-1 which depends on the strength of both the Hubbard interaction U and the core-hole potential Q. For Q <~ U_c/2 alpha decreases with increasing U and vanishes at the transition (U -> U_c) leading to a symmetric peak in the insulating phase. For Q >~ U_c/2, alpha remains finite close to the transition, but the integrated intensity of the power-law vanishes and there is no associated peak in the insulator. The weight and position of the remaining peaks in the spectra can be understood within a molecular orbital approach.Comment: 5 pages, 6 figure

A new neutron study of the short range order inversion in Fe1−x_{1-x}Crx_x

We have performed new neutron diffuse scattering measurements in Fe$_{1-x}$Cr$_x$ solid solutions, in a concentration range 0$<$x$<$0.15, where the atomic distribution shows an inversion of the short range order. By optimizing the signal-background ratio, we obtain an accurate determination of the concentration of inversion x$_0$ =0.110(5). We determine the near neighbor atomic short range order parameters and pair potentials, which change sign at x$_0$. The experimental results are compared with previous first principle calculations and atomistic simulations.Comment: 6 pages; 6 figure

Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra

We study Fermi edge singularities in photo-absorption spectra of generic mesoscopic systems such as quantum dots or nanoparticles. We predict deviations from macroscopic-metallic behavior and propose experimental setups for the observation of these effects. The theory is based on the model of a localized, or rank one, perturbation caused by the (core) hole left behind after the photo-excitation of an electron into the conduction band. The photo-absorption spectra result from the competition between two many-body responses, Anderson's orthogonality catastrophe and the Mahan-Nozieres-DeDominicis contribution. Both mechanisms depend on the system size through the number of particles and, more importantly, fluctuations produced by the coherence characteristic of mesoscopic samples. The latter lead to a modification of the dipole matrix element and trigger one of our key results: a rounded K-edge typically found in metals will turn into a (slightly) peaked edge on average in the mesoscopic regime. We consider in detail the effect of the "bound state" produced by the core hole.Comment: 16 page

Magnetic Field Effects on Quasiparticles in Strongly Correlated Local Systems

We show that quasiparticles in a magnetic field of arbitrary strength $H$ can be described by field dependent parameters. We illustrate this approach in the case of an Anderson impurity model and use the numerical renormalization group (NRG) to calculate the renormalized parameters for the levels with spin $\sigma$, $\tilde\epsilon_{\mathrm{d},\sigma}(H)$, resonance width $\tilde\Delta(H)$ and the effective local quasiparticle interaction $\tilde U(H)$. In the Kondo or strong correlation limit of the model the progressive de-renormalization of the quasiparticles can be followed as the magnetic field is increased. The low temperature behaviour, including the conductivity, in arbitrary magnetic field can be calculated in terms of the field dependent parameters using the renormalized perturbation expansion. Using the NRG the field dependence of the spectral density on higher scales is also calculated.Comment: 15 pages, 17 figure

Observation of metastable hcp solid helium

We have produced and observed metastable solid helium-4 below its melting pressure between 1.1 K and 1.4 K. This is achieved by an intense pressure wave carefully focused inside a crystal of known orientation. An accurate density map of the focal zone is provided by an optical interferometric technique. Depending on the sample, minimum density achieved at focus corresponds to pressures between 2 and 4 bar below the static melting pressure. Beyond, the crystal undergoes an unexpected instability much earlier than the predicted spinodal limit. This opens a novel opportunity to study this quantum crystal in an expanded metastable state and its stability limits.Comment: deuxi\`eme versio

The Coulomb impurity problem in graphene

We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice; (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation, namely bound state formation and strong renormalization of the van Hove singularities.Comment: 3 Figures; minor typo corrections and minor update in Fig. 3

Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

Sum Rules and Ward Identities in the Kondo Lattice

We derive a generalized Luttinger-Ward expression for the Free energy of a many body system involving a constrained Hilbert space. In the large $N$ limit, we are able to explicity write the entropy as a functional of the Green's functions. Using this method we obtain a Luttinger sum rule for the Kondo lattice. One of the fascinating aspects of the sum rule, is that it contains two components, one describing the heavy electron Fermi surface, the other, a sea of oppositely charged, spinless fermions. In the heavy electron state, this sea of spinless fermions is completely filled and the electron Fermi surface expands by one electron per unit cell to compensate the positively charged background, forming a ``large'' Fermi surface. Arbitrarily weak magnetism causes the spinless Fermi sea to annihilate with part of the Fermi sea of the conduction electrons, leading to a small Fermi surface. Our results thus enable us to show that the Fermi surface volume contracts from a large, to a small volume at a quantum critical point. However, the sum rules also permit the possible formation of a new phase, sandwiched between the antiferromagnet and the heavy electron phase, where the charged spinless fermions develop a true Fermi surface.Comment: 24 pages, 4 figures. Version two contains a proof of the "Entropy formula" which connects the entropy directly to the Green's functions. Version three contains corrections to typos and a more extensive discussion of the physics at finite