Functional integral approach to the single impurity Anderson model

Recently, a functional integral representation was proposed by Weller [1], in which the fermionic fields strictly satisfy the constraint of no double occupancy at each lattice site. This is achieved by introducing spin dependent Bose fields. The functional integral method is applied to the single impurity Anderson model both in the Kondo and mixed-valence regime. Thef-electron Green's function and susceptibility are calculated using an Ising-like representation for the Bose fields. We discuss the difficulty to extract a spectral function from the knowledge of the imaginary time Green's function. The results are compared with NCA calculations.     

A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ_c, the GFL [LM] phase occurring for δ<δ_c [ δ>δ_c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ_c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ_c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω_m ⁰ for fixed gaps δ/ω_m ⁰, where ω_m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω_m ⁰ ≫δ/ω_m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω_m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM.     

Hamiltonian map approach to 1D Anderson model

A one-dimensional diagonal tight binding electronic system is analyzed with the Hamiltonian map approach to study analytically the inverse localization length of an infinite sample. Both the uncorrelated and the dichotomic correlated random potential sequences are considered in the evaluations of the inverse localization length. Analytical expressions for the invariant measure or the angle density distribution are the main motivation of this work in order to derive analytical results. The well-known uncorrelated weak disorder result of the inverse localization length is derived with a clear procedure. In addition, an analytical expression for high disorder is obtained near the band edge. It is found that the inverse localization length goes to 1 in this limit. Following the procedure used in the uncorrelated situation, an analytical expression for the inverse localization length is also obtained for the dichotomic correlated sequence in the small disorder situation.     

Chebyshev expansion approach to the AC conductivity of the Anderson model

We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical conductivity of non-interacting electrons in a random potential (Anderson model) on large three-dimensional clusters. For low frequency the data follows the analytically expected power-law behaviour with an exponent that depends on disorder and has its minimum near the metal-insulator transition, where also the extrapolated DC conductivity continuously goes to zero. In view of the general applicability of the Chebyshev approach we briefly discuss its formulation for interacting quantum systems.Received: 6 June 2004, Published online: 12 August 2004PACS: 78.20.Bh Theory, models, and numerical simulation - 72.15.Rn Localisation effects (Anderson or weak localisation) - 05.60.Gg Quantum transport     

Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model

We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.     

Non-equilibrium STLS approach to transport properties of single impurity Anderson model

In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron–electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in the non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current–voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron–electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U²$U^2$ IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior.     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Real-space renormalisation approach to the Anderson localisation

A real-space renormalisation method is proposed for random systems. The equation for the Green function in real space is reduced to that for the Green function in renormalised space after the nth decimation transformation to obtain the renormalised Hamiltonian.     

New many body perturbation method and the Hubbard model

By adapting the functional derivative method developed by Kadanoff and Baym to the Hubbard model, a new perturbation method is formulated. The unperturbed state is defined by the two equations which yield Hubbard's results, while the remainder is given by functional derivatives of the Green's functions which are shown to generate a complete perturbation series. Advantages of this method are discussed.     

Relativistic many body approach for unstable nuclei and supernova

We study the properties of unstable nuclei and the equations of state of nuclear matter in the framework of the relativistic many body theory. We take the relativistic mean field (RMF) theory as a phenomenological theory with several parameters, whose form is constrained by the successful microscopic theory (RBHF), and whose values are extracted by using the experimental values of unstable nuclei. We find the outcome with the newly obtained parameter set (TMA) is promising in comparison with various experimental data. We study also the neutron star profiles with the equation of state of nuclear matter with the use of TMA.     

Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained. Received 19 December 2002 Published online 14 March 2003     

Rb Bose-Einstein condensate with tunable interaction: A quantum many body approach

We present a quantum many body approach with van der Waal type of interaction to achieve ⁸⁵Rb Bose-Einstein condensate with tunable interaction which has been produced by magnetic field induced Feshbach resonance in the JILA experiment.     

An elementary approach towards the Anderson transition

Approximation equations are motivated to describe the dynamical conductivity of a non interacting electron gas moving in a random potential. The equations are shown to yield an Anderson transition with a mobility decreasing continuously to zero on one side and a polarizability diverging on the other side of the mobility edge.