Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large $U$. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.Comment: 4 pages, 2 figure

Structure and transport in multi-orbital Kondo systems

We consider Kondo impurity systems with multiple local orbitals, such as rare earth ions in a metallic host or multi--level quantum dots coupled to metallic leads. It is shown that the multiplet structure of the local orbitals leads to multiple Kondo peaks above the Fermi energy $E_F$, and to ``shadow'' peaks below $E_F$. We use a slave boson mean field theory, which recovers the strong coupling Fermi liquid fixed point, to calculate the Kondo peak positions, widths, and heights analytically at T=0, and NCA calculations to fit the temperature dependence of high--resolution photoemission spectra of Ce compounds. In addition, an approximate conductance quantization for transport through multi--level quantum dots or single--atom transistors in the Kondo regime due to a generalized Friedel sum rule is demonstrated.Comment: 4 pages, 3 figures. Invited article, 23rd International Conference on Low Temperature Physics LT23, Hiroshima, Japan 200

The on-shell self-energy of the uniform electron gas in its weak-correlation limit

The ring-diagram partial summation (or RPA) for the ground-state energy of the uniform electron gas (with the density parameter $r_s$) in its weak-correlation limit $r_s\to 0$ is revisited. It is studied, which treatment of the self-energy $\Sigma(k,\omega)$ is in agreement with the Hugenholtz-van Hove (Luttinger-Ward) theorem $\mu-\mu_0= \Sigma(k_{\rm F},\mu)$ and which is not. The correlation part of the lhs h as the RPA asymptotics $a\ln r_s +a'+O(r_s)$ [in atomic units]. The use of renormalized RPA diagrams for the rhs yields the similar expression $a\ln r_s+a''+O(r_s)$ with the sum rule $a'= a''$ resulting from three sum rules for the components of $a'$ and $a''$. This includes in the second order of exchange the sum rule $\mu_{2{\rm x}}=\Sigma_{2{\rm x}}$ [P. Ziesche, Ann. Phys. (Leipzig), 2006].Comment: 19 pages, 10 figure

Bosonization of Fermi liquids

We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.Comment: 42 pages, RevteX, preprint UIUC (1993

Evaluation of the optical conductivity tensor in terms of contour integrations

For the case of finite life-time broadening the standard Kubo-formula for the optical conductivity tensor is rederived in terms of Green's functions by using contour integrations, whereby finite temperatures are accounted for by using the Fermi-Dirac distribution function. For zero life-time broadening, the present formalism is related to expressions well-known in the literature. Numerical aspects of how to calculate the corresponding contour integrals are also outlined.Comment: 8 pages, Latex + 2 figure (Encapsulated Postscript

Formation of atom wires on vicinal silicon

The formation of atomic wires via pseudomorphic step-edge decoration on vicinal silicon surfaces has been analyzed for Ga on the Si(112) surface using Scanning Tunneling Microscopy and Density Functional Theory calculations. Based on a chemical potential analysis involving more than thirty candidate structures and considering various fabrication procedures, it is concluded that pseudomorphic growth on stepped Si(112), both under equilibrium and non-equilibrium conditions, must favor formation of Ga zig-zag chains rather than linear atom chains. The surface is non-metallic and presents quasi-one dimensional character in the lowest conduction band.Comment: submitte

Damping of zero sound in Luttinger liquids

We calculate the damping gamma_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k^2 / 2 m at zero temperature. For wave-vectors | q| /k_F small compared with F we find to leading order gamma_q = v_F^{-1} m^{-2} Y (F) | q |^3, where v_F is the Fermi velocity, k_F is the Fermi wave-vector, and Y (F) is proportional to F^3 for small F. We also show that zero-sound damping leads to a finite maximum proportional to |k - k_F |^{-2 + 2 eta} of the charge peak in the single-particle spectral function, where eta is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_{0.3}MoO_3.Comment: final version as published; with more technical details; we have added a discussion of recent work which appeared after our initial cond-mat posting; 13 pages, 5 figure

Violation of Luttinger's Theorem in the Two-Dimensional t-J Model

We have calculated the high temperature series for the momentum distribution function n_k of the 2D t-J model to 12th order in inverse temperature. By extrapolating the series to T=0.2J we searched for a Fermi surface of the 2D t-J model. We find that three criteria used for estimating the location of a Fermi surface violate Luttinger's Theorem, implying the 2D t-J model does not have an adiabatic connection to a non-interacting model.Comment: 4 pages, 5 figures. Version with grayscale figures available upon reques

A Supersymmetry approach to billiards with randomly distributed scatterers

The density of states for a chaotic billiard with randomly distributed point-like scatterers is calculated, doubly averaged over the positions of the impurities and the shape of the billiard. Truncating the billiard Hamiltonian to a N x N matrix, an explicit analytic expression is obtained for the case of broken time-reversal symmetry, depending on rank N of the matrix, number L of scatterers, and strength of the scattering potential. In the strong coupling limit a discontinuous change is observed in the density of states as soon as L exceeds N

Two-dimensional array of magnetic particles: The role of an interaction cutoff

Based on theoretical results and simulations, in two-dimensional arrangements of a dense dipolar particle system, there are two relevant local dipole arrangements: (1) a ferromagnetic state with dipoles organized in a triangular lattice, and (2) an anti-ferromagnetic state with dipoles organized in a square lattice. In order to accelerate simulation algorithms we search for the possibility of cutting off the interaction potential. Simulations on a dipolar two-line system lead to the observation that the ferromagnetic state is much more sensitive to the interaction cutoff $R$ than the corresponding anti-ferromagnetic state. For $R \gtrsim 8$ (measured in particle diameters) there is no substantial change in the energetical balance of the ferromagnetic and anti-ferromagnetic state and the ferromagnetic state slightly dominates over the anti-ferromagnetic state, while the situation is changed rapidly for lower interaction cutoff values, leading to the disappearance of the ferromagnetic ground state. We studied the effect of bending ferromagnetic and anti-ferromagnetic two-line systems and we observed that the cutoff has a major impact on the energetical balance of the ferromagnetic and anti-ferromagnetic state for $R \lesssim 4$. Based on our results we argue that $R \approx 5$ is a reasonable choice for dipole-dipole interaction cutoff in two-dimensional dipolar hard sphere systems, if one is interested in local ordering.Comment: 8 page