The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials

We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or "the algebra of supersymmetric quantum mechanics", and its Fock representation. The model offers some freedom in the choice of a position and a momentum operator, leading to a free model parameter gamma. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials C_n with parameter gamma^2. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillator model.Comment: Minor changes and some additional references added in version

Effective Crystalline Electric Field Potential in a j-j Coupling Scheme

We propose an effective model on the basis of a $j$-$j$ coupling scheme to describe local $f$-electron states for realistic values of Coulomb interaction $U$ and spin-orbit coupling $\lambda$, for future development of microscopic theory of magnetism and superconductivity in $f^n$-electron systems, where $n$ is the number of local $f$ electrons. The effective model is systematically constructed by including the effect of a crystalline electric field (CEF) potential in the perturbation expansion in terms of $1/\lambda$. In this paper, we collect all the terms up to the first order of $1/\lambda$. Solving the effective model, we show the results of the CEF states for each case of $n$=2$\sim$5 with $O_{\rm h}$ symmetry in comparison with those of the Stevens Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF energy levels in an intermediate coupling region with $\lambda/U$ in the order of 0.1 corresponding to actual $f$-electron materials between the $LS$ and $j$-$j$ coupling schemes. Note that the relevant energy scale of $U$ is the Hund's rule interaction. It is found that the CEF energy levels in the intermediate coupling region can be quantitatively reproduced by our modified $j$-$j$ coupling scheme, when we correctly take into account the corrections in the order of $1/\lambda$ in addition to the CEF terms and Coulomb interactions which remain in the limit of $\lambda$=$\infty$. As an application of the modified $j$-$j$ coupling scheme, we discuss the CEF energy levels of filled skutterudites with $T_{\rm h}$ symmetry.Comment: 12 pages, 7 figures. Typeset with jpsj2.cl

Full configuration interaction approach to the few-electron problem in artificial atoms

We present a new high-performance configuration interaction code optimally designed for the calculation of the lowest energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a single-particle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted and correlation becomes dominant. Comparison with previous Quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.Comment: RevTeX 4.0, 18 pages, 6 tables, 9 postscript b/w figures. Final version with new material. Section 6 on the excitation spectrum has been added. Some material has been moved to two appendices, which appear in the EPAPS web depository in the published versio

Short Time Behavior in De Gennes' Reptation Model

To establish a standard for the distinction of reptation from other modes of polymer diffusion, we analytically and numerically study the displacement of the central bead of a chain diffusing through an ordered obstacle array for times $t < O(N^2)$. Our theory and simulations agree quantitatively and show that the second moment approaches the $t^{1/4}$ often viewed as signature of reptation only after a very long transient and only for long chains (N > 100). Our analytically solvable model furthermore predicts a very short transient for the fourth moment. This is verified by computer experiment.Comment: 4 pages, revtex, 4 ps file

Microscopic Approach to Magnetism and Superconductivity of ff-Electron Systems with Filled Skutterudite Structure

In order to gain a deep insight into $f$-electron properties of filled skutterudite compounds from a microscopic viewpoint, we investigate the multiorbital Anderson model including Coulomb interactions, spin-orbit coupling, and crystalline electric field effect. For each case of $n$=1$\sim$13, where $n$ is the number of $f$ electrons per rare-earth ion, the model is analyzed by using the numerical renormalization group (NRG) method to evaluate magnetic susceptibility and entropy of $f$ electron. In order to make further step to construct a simplified model which can be treated even in a periodic system, we also analyze the Anderson model constructed based on the $j$-$j$ coupling scheme by using the NRG method. Then, we construct an orbital degenerate Hubbard model based on the $j$-$j$ coupling scheme to investigate the mechanism of superconductivity of filled skutterudites. In the 2-site model, we carefully evaluate the superconducting pair susceptibility for the case of $n$=2 and find that the susceptibility for off-site Cooper pair is clearly enhanced only in a transition region in which the singlet and triplet ground states are interchanged.Comment: 14 pages, 11 figures, Typeset with jpsj2.cl

Entanglement purification of unknown quantum states

A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from $N$ copies of a bipartite quantum system about which only partial information is known, for instance in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state $\rho^{(N)}$ of the $N$ copies of the quantum system is exchangeable, one can write down a simple general expression for $\rho^{(N)}$. We show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.Comment: 20 pages RevTeX 3.0 + 1 figure (encapsulated Postscript) Submitted to Physical Review

Analysis of OPM potentials for multiplet states of 3d transition metal atoms

We apply the optimized effective potential method (OPM) to the multiplet energies of the 3d$^n$ transition metal atoms, where the orbital dependence of the energy functional with respect to orbital wave function is the single-configuration HF form. We find that the calculated OPM exchange potential can be represented by the following two forms. Firstly, the difference between OPM exchange potentials of the multiplet states can be approximated by the linear combination of the potentials derived from the Slater integrals $F^2({\rm 3d,3d})$ and $F^4({\rm 3d,3d})$ for the average energy of the configuration. Secondly, the OPM exchange potential can be expressed as the linear combination of the OPM exchange potentials of the single determinants.Comment: 15 pages, 6 figures, to be published in J. Phys.

On the Origin of the -4.4 eV Band in CdTe(100)"

We calculate the bulk- (infinite system), (100)-bulk-projected- and (100)-Surface-projected Green's functions using the Surface Green's Function Matching method (SGFM) and an empirical tight-binding hamiltonian with tight-binding parameters (TBP) that describe well the bulk band structure of CdTe. In particular, we analyze the band (B--4) arising at --4.4 eV from the top of the valence band at $\Gamma$ according to the results of Niles and H\"ochst and at -4.6 eV according to Gawlik {\it et al.} both obtained by Angle-resolved photoelectron spectroscopy (ARPES). We give the first theoretical description of this band.Comment: 17 pages, Rev-TEX, CIEA-Phys. 02/9

Phase transitions in the boson-fermion resonance model in one dimension

We study 1D fermions with photoassociation or with a narrow Fano-Feshbach resonance described by the Boson-Fermion resonance model. Using thebosonization technique, we derive a low-energy Hamiltonian of the system. We show that at low energy, the order parameters for the Bose Condensation and fermion superfluidity become identical, while a spin gap and a gap against the formation of phase slips are formed. As a result of these gaps, charge density wave correlations decay exponentially in contrast with the phases where only bosons or only fermions are present. We find a Luther-Emery point where the phase slips and the spin excitations can be described in terms of pseudofermions. This allows us to provide closed form expressions of the density-density correlations and the spectral functions. The spectral functions of the fermions are gapped, whereas the spectral functions of the bosons remain gapless. The application of a magnetic field results in a loss of coherence between the bosons and the fermion and the disappearance of the gap. Changing the detuning has no effect on the gap until either the fermion or the boson density is reduced to zero. Finally, we discuss the formation of a Mott insulating state in a periodic potential. The relevance of our results for experiments with ultracold atomic gases subject to one-dimensional confinement is also discussed.Comment: 31 pages, 8 EPS figures, RevTeX 4, long version of cond-mat/050570

Unscreened Hartree-Fock calculations for metallic Fe, Co, Ni, and Cu from ab-initio Hamiltonians

Unscreened Hartree-Fock approximation (HFA) calculations for metallic Fe, Co, Ni, and Cu are presented, by using a quantum-chemical approach. We believe that these are the first HFA results to have been done for crystalline 3d transition metals. Our approach uses a linearized muffin-tin orbital calculation to determine Bloch functions for the Hartree one-particle Hamiltonian, and from these obtains maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and two-particle Coulomb matrix elements are calculated. The resulting second-quantized multi-band Hamiltonian with ab-initio parameters is studied within the simplest many-body approximation, namely the unscreened, self-consistent HFA, which takes into account exact exchange and is free of self-interactions. Although the d-bands sit considerably lower within HFA than within the local (spin) density approximation L(S)DA, the exchange splitting and magnetic moments for ferromagnetic Fe, Co, and Ni are only slightly larger in HFA than what is obtained either experimentally or within LSDA. The HFA total energies are lower than the corresponding LSDA calculations. We believe that this same approach can be easily extended to include more sophisticated ab-initio many-body treatments of the electronic structure of solids.Comment: 11 papes, 7 figures, 5 table