Quasiparticle Formalism Research Articles

A unified quasiparticle approach to the theory of strongly correlated electron liquids

Landau’s quasiparticle formalism is generalized to describe a wide class of strongly correlated Fermi systems, in addition to conventional Fermi liquids. This class includes (i) so-called marginal exemplars and (ii) systems that harbor interaction-driven flat bands, in both of which manifestations of non-Fermi-liquid behavior are well documented. Specifically, the advent of such flat bands is attributed to a spontaneous topological rearrangement of the Landau state that supplements the conventional Landau quasiparticle picture with a different set of quasiparticles, the so-called fermion condensate, whose single-particle spectrum is dispersionless. The celebrated Landau–Luttinger theorem is extended to marginal Fermi liquids, in which the density of the augmented quasiparticle system is shown to coincide with the particle density. On the other hand, the total density of a system hosting an interaction-driven flat band turns out to be the sum of the densities of the two quasiparticle subsystems: the Landau-like component and the fermion condensate. We demonstrate that within the framework of the scenario proposed, a long-standing problem faced by theories of D-wave superconductivity in cuprates, namely a consistent explanation of the so-called Uemera plot, can be naturally resolved.

Effect of propagator renormalization on the band gap of insulating solids

We present momentum-resolved spectral functions and band gaps from bare and self-consistent second-order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasiparticle formalism used on top of bare second-order perturbation theory, no unphysical behavior of the band gap is observed. Our implementation of a fully self-consistent, $\mathrm{\ensuremath{\Phi}}$-derivable, and thermodynamically consistent finite-temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean-field theory and self-energy embedding theories can be implemented.

Condensation ofNbosons: Microscopic approach to fluctuations in an interacting Bose gas

We present a microscopic derivation of the master equation for the condensate density matrix for an interacting Bogoliubov-Bose gas of N atoms. We choose the interaction Hamiltonian in a special way that substantially simplifies the master equation, yielding no coupling between diagonal and off-diagonal terms. The present formulation allows us to solve the problem analytically in a steady state and obtain the expression for the distribution function and equilibrium condensate fluctuations. For the first two central moments, our results are equivalent to those obtained in the canonical-ensemble quasiparticle formalism [V. V. Kocharovsky, Vl. V. Kocharovsky, and M. O. Scully, Phys. Rev. Lett. 84, 2306 (2000); Phys. Rev. A 61, 053606 (2000)], in the low-temperature range where these papers are valid, but also give an accurate description at high temperatures. The present analysis for an interacting Bose gas is as accurate as the master equation approach of Kocharovsky et al. [Phys. Rev. A 61, 023609 (2000)] is for an ideal gas.

Fluctuation statistics of mesoscopic Bose-Einstein condensates: Reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma

The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. For the case of a harmonic trap, we obtain an analytic expression for the condensate particle number that is very accurate at all temperatures, when compared with numerical canonical ensemble results. Applying a similar generalized grand canonical treatment to the variance, we obtain an accurate result only below the critical temperature. Analytic results are found for all higher moments of the fluctuation distribution by employing the stochastic path integral formalism, with excellent accuracy. We further discuss a hybrid treatment, which combines the master equation and stochastic path integral analysis with results obtained based on the canonical ensemble quasiparticle formalism [Kocharovsky et al., Phys. Rev. A 61, 053606 (2000)], producing essentially perfect agreement with numerical simulation at all temperatures.

Influence of oxygen on optical properties of Si nanocrystallites

The influence of oxygen on optical absorption spectra, radiative lifetimes, and localization of states is analyzed within the quasiparticle formalism based on the GW approximation for defect-free Si nanocrystallites. Passivation with hydroxyls and oxide coverage have significant influence on the spatial distribution of the highest-occupied and lowest-unoccupied molecular orbitals as well as on the radiative lifetimes. Oxidation blueshifts the onset of absorption, whereas oxide coverage and passivation with hydroxyls tend to redshift it. The indirect-gap nature of the optical transitions in Si bulk is transferred to the Si nanocrystallites independently of the oxygen contents.

Transdisciplinary aspects of diffusion and magnetocaloric effect

The modeling of magnetocaloric effect (MCE) based on quasiparticle formalism was used to show a possibility to increase our knowledge of diffusion and phase transitions by a transdisciplinary scientific approach. Generalized understanding of diffusion and of some phase transitions was suggested. New relations between MCE and elastic parameters of materials, obtained from modeling procedure, were presented. The paper contains also the short discussion of a necessity to use hypercomplex mathematics in modeling of magnetic processes and specifically in a modeling of MCE. Some remarks concerning nanomaterials are added.

Quasiparticles in the theory of fermion condensation

It is shown that Landau’s quasiparticle formalism continues to work in systems with a fermion condensate. In the case of a finite system this formalism is suitable for describing the restructuring of states at the Fermi surface. It also works in an infinite system, and the idea of quasiparticles at low temperature as well-defined excitations at the Fermi surface remains valid. The quasiparticle lifetime is directly proportional to the temperature, and the density of states is inversely proportional to the temperature.

Inverse photoemission study of non-reconstructed Si(111) surfaces: a comparison between HSi(111) 1 × 1 and As:Si(111) 1 × 1

The lower conduction-band states of Si(111) have been measured by k |-resolved inverse photoelectron spectroscopy (KRIPES) on non-reconstructed surfaces obtained either by saturating the dangling bonds with atomic hydrogen or by replacing the Si surface atoms with As atoms. On the HSi(111)1 × 1 surface, two conduction bands are measured whose asymmetry in the q̄G-M̄ direction reveals their bulk character. The same conduction band states are also measured on the As:Si(111)1 × 1 surface, however at lower energies as a result of the higher electronegativity of the As atoms. These latter data are in excellent agreement with recent calculations using the quasi-particle formalism.

Electronic structure of Si(100)c(4 x 2) calculated within the GW approximation.

The electronic structure of the Si(100)c(4\ifmmode\times\else\texttimes\fi{}2) surface has been calculated using a quasiparticle formalism in which the self-energy is evaluated in the GW approximation. The calculated surface state dispersions and band gaps are in good agreement with experiments. The results support the existence of correlated dimer buckling at room temperature. The equilibrium c(4\ifmmode\times\else\texttimes\fi{}2) surface obtained from total-energy calculations is 0.14 eV/dimer lower in energy than the 2\ifmmode\times\else\texttimes\fi{}1 symmetric dimer surface, exhibits a dimer buckling of 0.69 \AA{}, and has a surface energy of 1.39 eV/(1\ifmmode\times\else\texttimes\fi{}1).

Calculation of beta-decay half-lives of proton-rich nuclei of intermediate mass.

We present the results of a calculation of the beta-decay half-lives of several proton-rich even-even nuclei of intermediate mass: 74Sr, 76Sr, 78Zr, 80Zr, 84Mo, 86Mo, 88Ru, 90Ru, 92Pd, and 96Cd. The calculation is based upon the random phase approximation with the quasiparticle formalism and takes into account the residual particle-particle interaction.

Perturbation theory of the Fermi surface in a quantum liquid. A general quasiparticle formalism and one-dimensional systems

We develop a perturbation theory formalism for the theory of the Fermi surface in a Fermi liquid of particles interacting via a bounded short-range repulsive pair potential. The formalism is based on the renormalization group and provides a formal expansion of the large-distance Schwinger functions in terms of a family of running couplings consisting of one- and two-body quasiparticle potentials. The flow of the running couplings is described in terms of a beta function, which is studied to all orders of perturbation theory and shown to obey, in thenth order,n! bounds. The flow equations are written in general dimensiond⩾1 for the spinless case (for simplicity). The picture that emerges is that on a large scale the system looks like a system of fermions interacting via aδ-like interaction potential (i.e., a potential approaching 0 everywhere except at the origin, where it diverges, although keeping the integral bounded); the theory is not asymptotically free in the usual sense and the freedom mechanism is thus more delicate than usual: the technical problem of dealing with unbounded effective potentials is solved by introducing a mathematically precise notion ofquasiparticles, which turn out to be natural objects with finite interaction even when the physical potential diverges as a deltalike function. A remarkable kind of gauge symmetry is associated with the quasiparticles. To substantiate the analogy with the quasiparticle theory we discuss the mean field theory using our notion of quasiparticles: the resulting self-consistency relations are closely reminiscent of those of the BCS model. The formalism seems suited for a joint theory of normal states of Fermi liquids and of BCS states: the first are associated with the trivial fixed point of our flow or with nearby nontrivial fixed points (or invariant sets) and the second may naturally correspond to really nontrivial fixed points (which may nevertheless turn out to be accessible to analysis because the BCS state is a quasi free state, hence quite simple, unlike the nontrivial fixed points of field theory). Thed=1 case is deeply different from thed> 1 case, for our spinless fermions: we can treat it essentially completely for small coupling. The system is not asymptotically free and presents anomalous renormalization group flow with a vanishing beta function, and the discontinuity of the occupation number at the Fermi surface is smoothed by the interaction (remaining singular with a coupling-dependent singularity of power type with exponent identified with the anomalous dimension). Finally, we present a heuristic discussion of the theory for the flow of the running coupling constants in spinlessd> 1 systems: their structure is simplified further and the relevant part of the running interaction is precisely the interaction between pairs of quasiparticles which we identify with the Cooper pairs of superconductivity. The formal perturbation theory seems to have a chance to work only if the interaction between the Cooper pairs is repulsive: and to second order we show that in the spin-0 case this happens if the physical potential is repulsive. Our results indicate the possibility of the existence of a normal Fermi surface only if the interaction is repulsive.

Charge excitations in the one-dimensional Hubbard model.

On the basis of the Bethe ansatz solution, the characteristic properties of charge excitations are investigated for the one-dimensional Hubbard model by inserting a charged hole into the Mott insulator. The density of states for the charged hole shows divergent behavior in the lower-energy region, whose connection is discussed analytically with the compressibility and magnitude of the Hubbard gap. Momentum-dependent susceptibility is also investigated within the framework of the quasiparticle formalism in the Bethe ansatz method. The logarithmic anomaly of the susceptibilty for the charged hole near 4${k}_{F}$ (${k}_{F}$ being the Fermi momentum in the noninteracting case) is considerably enhanced in the vicinity of the Mott insulating phase, while it is suppressed at the insulating phase due to the formation of the Hubbard gap.

Application of the Dyson-type non-unitary representation of the self-consistent collective-coordinate method to simple models (II). O(4) Model

The Dyson-type non-unitary representation of the self-consistent collective-coordinate (SCC) method is applied to a solvable O(4) model which is one of the simplest examples of superconducting cases. The particle-number non-conservation problem in the quasiparticle formalism is approximately solved within the framework of the SCC method by taking into account the coupling effect of the pairing-rotational mode. The numerical calculations show that the present Dyson-type SCC method gives as good results as the original unitary version.

Coupled-cluster method in Fock space. I. General formalism.

The problem of finding the spectrum of the Fock-space Hamiltonian \ifmmode \hat{H}\else \^{H}\fi{} for a system of many fermions is analyzed. The quasiparticle formalism is employed, with ``holes'' and ``particles'' defined with respect to some N-particle determinantal wave function (the model vacuum). The basic idea behind the proposed approach is to perform a similarity transformation of Hamiltonian \ifmmode \hat{H}\else \^{H}\fi{}, such that the resulting effective Hamiltonian \ifmmode \hat{G}\else \^{G}\fi{} is, unlike \ifmmode \hat{H}\else \^{H}\fi{}, a quasiparticle-number--conserving operator. It is shown that eigenvalues of \ifmmode \hat{G}\else \^{G}\fi{}, corresponding to small numbers of quasiparticles (0,1,2) can be easily calculated. This is equivalent to finding eigenvalues of \ifmmode \hat{H}\else \^{H}\fi{} for certain states of N, N\ifmmode\pm\else\textpm\fi{}1, and N\ifmmode\pm\else\textpm\fi{}2 particles. The construction of the operator transforming \ifmmode \hat{H}\else \^{H}\fi{} into \ifmmode \hat{G}\else \^{G}\fi{} (the wave operator) stems from an analysis of the structure of the algebra of linear operators acting in a (finite-dimensional) Fock space. The exponential Ansatz for the wave operator is used, resulting in a generalization of the coupled-cluster (CC) method of Coester [Nucl. Phys. 7, 421 (1958)]. The generalized CC equations determining the wave operator, and equations determining the effective Hamiltonian \ifmmode \hat{G}\else \^{G}\fi{}, are presented in a diagrammatic form. An effort has been made to obtain a concise notation for expressing these equations in an algebraic form. Approximation schemes, necessary for practical applications of the proposed method, are also studied.

Atomic shell operators in the quasiparticle formalism

The operators acting within the ln (any n>or=0) atomic shells are studied in the quasiparticle scheme of Armstrong and Judd (1970) Lie algebra generated by operators involving products of more than two creation or annihilation operators are obtained. The introduction of operators exchanging odd and even states of two quasiparticle spaces proves to be very useful in this study.

Quasiparticle effects in the two-body photodisintegration of 4He

The total cross sections for the reactions 4He(γ, n) 3He and 4He(γ, p) 3H are calculated for photon energies between 50 MeV and 150 MeV in a quasiparticle formalism, leading to a simple interpretation for the γ-absorption mechanism. Results are compared with shell model calculations.

Relation between the interacting boson approximation and the quasiparticle formalism

A direct relationship is demonstrated between the interacting boson approximation and the conventional quasiparticle formalism. Numerical calculations are carried out for the Sn isotopes using a Hamiltonian derived from a realistic nucleon-nucleon interaction.

Application of the quasiparticle formalism to neutron-deuteron scattering with local soft-core nucleon-nucleon potentials

The quasiparticle approach which exactly reduces the three-body Faddeev formalism to an effective two-body theory is a general starting point for deriving approximation schemes. Practical methods, currently in use for solving the effective two-body equations, follow from it as special cases. A new procedure is proposed which is well suited for local nucleon-nucleon interactions containing repulsion. Its effectiveness is tested by calculating the triton binding energy and elastic neutron-deuteron scattering data for the soft-core potentials of Malfliet and Tjon. Particular emphasis is laid on extracting the influence of higher subsystem partial wave contributions of these potentials.

Calculations in the50<N,Z<82region with an interaction derived from the Tabakin potential

The region of the Periodic Table with $50\ensuremath{\le}Z$, $N\ensuremath{\le}82$ is studied using fixed single particle energies and a semirealistic effective interaction derived from the Tabakin potential. All the free parameters are determined by fitting the data on the odd-mass Sn isotopes and $N=82$ isotones. A conventional quasiparticle formalism is then used to study the structure of a range of spherical nuclei near the $N=82$ and the $Z=50$ magic numbers. A deformed Hartree-Fock plus BCS method is used to obtain the structure and electromagnetic properties of deformed nuclei, particularly the neutron-deficient even Ba isotopes. Prolate deformation is found to be favored. In the Ba isotopes, although neutrons have BCS correlation, the protons develop an energy gap between occupied and unoccupied orbitals due to the Hartree-Fock field itself. The proton orbitals are then tested through spectroscopic calculations in La isotopes. Both for spherical and deformed nuclei, agreement between theory and experiment is very satisfactory.NUCLEAR STRUCTURE Mass region $100<A<150$; calculated levels, $J$, $\ensuremath{\pi}$, and other properties. Semirealistic forces; combination of deformed Hartree-Fock and BCS methods.

Quasiparticle Formalism and Atomic Shell Theory. II. Mixed Configurations

The quasiparticle technique and formalism of an earlier paper is extended to describe general mixed configurations. The main features of the equivalent electron case are preserved, viz., a loss of spin quantum number and particle number, compensated by a rich classificatory scheme, and general operator-matrix-element evaluation without the use of coefficients of fractional parentage.