Adaptation of the Landau-Migdal quasiparticle pattern to strongly correlated Fermi systems

A quasiparticle pattern advanced in Landau’s first article on Fermi-liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi-Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exceptional state whose spectrum of single-particle excitations exhibits a completely flat portion at zero temperature. Analysis of the evolution of the temperature dependence of the single-particle spectrum yields results that provide a natural explanation of classical behavior of this class of Fermi systems in the QCP region.     

Fermi surface and quasiparticle dynamics of Na0.7CoO2 investigated by angle-resolved photoemission spectroscopy

We present the first angle-resolved photoemission study of Na0.7CoO2, the host material of the superconducting NaxCoO2.nH(2)O series. Our results show a hole-type Fermi surface, a strongly renormalized quasiparticle band, a small Fermi velocity, and a large Hubbard U. The quasiparticle band crosses the Fermi level from M toward Gamma suggesting a negative sign of effective single-particle hopping t(eff) (about 10 meV) which is on the order of magnetic exchange coupling J in this system. Quasiparticles are well defined only in the T-linear resistivity (non-Fermi-liquid) regime. Unusually small single-particle hopping and unconventional quasiparticle dynamics may have implications for understanding the phase of matter realized in this new class of a strongly interacting quantum system.     

Nature of quasiparticles in itinerant correlated electron systems with geometrical frustration

Using the exact diagonalization technique, we study the effect of geometrical frustration on single-particle, spin and charge excitations in the Hubbard model in a metallic state close to half-filling. As the frustration increases, the magnetic order in the system is suppressed and the peak in the single-particle spectrum becomes sharper, indicating enhanced quasiparticle formation. Careful examination of spin and charge excitations shows that increasing frustration also leads to the merge of spin and charge excitation energies to that of the single-particle excitation. This is consistent with a Fermi liquid having well-defined quasiparticles with both spin and charge characteristics. The calculated results show that geometrical frustration plays an important role in defining the nature of quasiparticles in itinerant correlated electron systems.     

Damping effects and the metal-insulator transition in a two-dimensional electron gas

The damping of single-particle degrees of freedom in strongly correlated two-dimensional Fermi systems is analyzed. Suppression of the scattering amplitude due to the damping effects is shown to play a key role in preserving the validity of the Landau-Migdal quasiparticle picture in a region of a phase transition associated with the divergence of the quasiparticle effective mass. The results of the analysis are applied to elucidate the behavior of the conductivity σ(T) of the two-dimensional dilute electron gas in the density region where it undergoes a metal-insulator transition.     

Flattening of single-particle spectra in strongly correlated electron systems and the violation of the Wiedemann-Franz law

The renormalization of the Wiedemann-Franz (WF) ratio in strongly correlated electron systems is analyzed within the Landau quasiparticle picture. We demonstrate that the WF law is violated: (i) at the quantum critical point, where the effective mass diverges, and (ii) beyond a point of fermion condensation, where the single-particle spectrum ∈(p) becomes flat. Results of the analysis are compared with available experimental data.     

High-energy kink in the single-particle spectra of the two-dimensional hubbard model

Employing dynamical cluster quantum Monte Carlo calculations we show that the single-particle spectral weight A(k,omega) of the one-band two-dimensional Hubbard model displays a high-energy kink in the quasiparticle dispersion followed by a steep dispersion of a broad peak similar to recent angle-resolved photoemission spectroscopy results reported for the cuprates. Based on the agreement between the Monte Carlo results and a simple calculation which couples the quasiparticle to spin fluctuations, we conclude that the kink and the broad spectral feature in the Hubbard model spectra is due to scattering with damped high-energy spin fluctuations.     

Flattening of single-particle spectra in strongly correlated electron systems and the violation of the Wiedemann-Franz law

The renormalization of the Wiedemann-Franz (WF) ratio in strongly correlated electron systems is analyzed within the Landau quasiparticle picture. We demonstrate that the WF law is violated: (i) at the quantum critical point, where the effective mass diverges, and (ii) beyond a point of fermion condensation, where the single-particle spectrum ∈(p) becomes flat. Results of the analysis are compared with available experimental data. The text was submitted by the authors in English.     

Finite Fermi systems theory and self-consistency relations

The self-consistent theory of the finite Fermi systems is outlined. This approach is based on the same Fermi liquid theory principles as the familiar theory for finite Fermi systems (FFS) by Migdal. We show that the basic Fermi system properties can be evaluated in terms of the quasiparticle Lagrangian L_q which incorporates the energy dependency effects. This Lagrangian is defined so that the corresponding Lagrange equations should coincide with the FFS theory equations of motion of the quasiparticles. The quasiparticle energy E_q defined in the terms of t he quasiparticle Lagrangian L_q according to the usual canonical rules is shown to be equal to the binding energy E_o of the system. For a given Lagrangian L_q the particle densities in nuclei, the nuclear single-particle spectra, the low-lying collective states (LCS) properties, and the amplitude of the interquasiparticle interaction are also evaluated. The suggested approach is compared with the Hartree-Fock theory with effective forces.     

Thermo field dynamics in the treatment of the nuclear pairing problem at finite temperature

The use of the thermo field dynamics, in dealing with the study of nuclear properties at finite temperature, is discussed for the case of a nuclear Hamiltonian which includes a single-particle term and a monopole pairing residual two-body interaction. The rules of the thermo field dynamics are applied to double the Hilbert space, thus accounting for the thermal occupation of single-particle states, and to construct dual spaces, both for single-particle (BCS) and collective (RPA) degrees of freedom. It is shown that the rules of the thermo field dynamics yield to a temperature dependence of the equations describing quasiparticle and phonon excitations which is similar to the one found in the more conventional finite temperature Wick's theorem approach, namely: by dealing with thermal averages.     

Absence of fermionic quasiparticles in the superfluid state of the attractive fermi gas

We calculate the effect of order parameter fluctuations on the fermionic single-particle excitations in the superfluid state of neutral fermions interacting with short-range attractive forces. We show that in dimensions D< or =3 the singular effective interaction between the fermions mediated by the gapless Bogoliubov-Anderson mode prohibits the existence of well-defined quasiparticles. We explicitly calculate the single-particle spectral function in the BEC regime in D=3 and show that in this case the quasiparticle residue and the density of states are logarithmically suppressed.     

Ground state correlations and structure of odd spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the phonon operators are not ideal boson operators. Calculating the exact commutators between the quasiparticle and phonon operators, one can take into account the Pauli principle corrections. Besides, the ground state correlations due to the quasiparticle interaction in the ground state influence the single-particle fragmentation as well. In this paper, we generalize the basic equations of the quasiparticle-phonon nuclear model to account for both effects mentioned. As an illustration of our approach, calculations on the structure of the low-lying states in ¹³³Ba have been performed. The text was submitted by the authors in English.     

Mean-field effects on neutrinoless double beta decay

Mean-field effects on the nuclear matrix elements involved in the neutrinoless double beta (0νββ) decay of several double-electron and double-positron emitters have been studied within the framework of the relativistic quark-confinement model and the quasiparticle random-phase approximation. The single-particle energies of the model space have been generated both by using the standard Woods-Saxon parametrization of the mean field and adjusting the quasiparticle spectra with the data from neutron- and proton-odd nuclei. The 0νββ rates are found to be much less affected by the energies of the mean-field orbitals than the rates of the two-neutrino double beta decay. The present study suggests that the extracted effective neutrino masses vary within a factor of two when using different realistic single-particle bases in the calculations.     

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green's function method. Taking the weakly bound nucleus ~(66)Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared. For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum. By switching off the pairing potential and/or the Hartree-Fock(HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential. The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here,especially for the partial waves with small angular momentum ?.     

The use of coherent states in the variational treatment of proton-neutron interactions

Coherent states are used as trial states to determine, variationally, the structure of the eigenvectors belonging to a schematic Hamiltonian consisting of single-particle, pairing and residual proton-neutron interaction terms. It is shown that the standard proton-neutron quasiparticle random-phase approximation (pn-QRPA) is recovered, as a variational theory, by replacing quasiparticle pair creation and annihilation operators by bosons. It is also shown that an exact, algebra preserving, mapping of the Hamiltonian is needed to describe the spectrum beyond the QRPA phase transition. The role of the spurious components of the trial wave functions is discussed. Received: 19 February 2002 / Accepted: 3 May 2002     

Single-particle self-energy and optical conductivity of the simplified Hubbard model

It is shown that the single-particle self-energy of the one and two-dimensional simplified Hubbard model exhibits different behavior characterized by Fermi-liquid, non-Fermi-liquid quasiparticle, or non-quasiparticle excitations, as a function of the strength of the on-site Coulomb repulsionU, temperature, and electron filling. For half-filled lattices, results for the optical conductivity indicate that the d.c. conductivity is zero for all temperatures andU>0.     

Topological crossovers near a quantum critical point

We study the temperature evolution of the single-particle spectrum ε-(p) and quasiparticle momentum distribution n(p) of homogeneous strongly correlated Fermi systems beyond a point where the necessary condition for stability of the Landau state is violated, and the Fermi surface becomes multi-connected by virtue of a topological crossover. Attention is focused on the different non-Fermi-liquid temperature regimes experienced by a phase exhibiting a single additional hole pocket compared with the conventional Landau state. A critical experiment is proposed to elucidate the origin of NFL behavior in dense films of liquid ³He.     

Spectral properties of the 2D Holstein polaron

The two-dimensional Holstein model is studied by means of direct Lanczos diagonalization preserving the full dynamics and quantum nature of phonons. We present numerical exact results for the single-particle spectral function, the polaronic quasiparticle weight, and the optical conductivity. The polaron band dispersion is derived both from exact diagonalization of small lattices and analytic calculation of the polaron self-energy.     

Breakup of quasiparticles in thin-film quantum wells

Quantum well states in thin films are commonly described in terms of a quasiparticle confined in a quantum box, but this single-particle picture can fail dramatically near a substrate band edge, as shown by this angle-resolved photoemission study. Atomically uniform Ag films are prepared on Ge(111) to facilitate accurate line shape and dispersion relation measurements. A quantum well peak is observed to split into two peaks near the Ge valence band edge. The unusual line shapes are shown to be due to many-body interactions and are quantitatively explained by a Green's function calculation.     

Pygmy dipole resonance in nuclei

A brief survey of the state of the modern microscopic theory of the so-called pygmy dipole resonance in nuclei is given—in particular, some unresolved problems are listed. It is emphasized that, in order to explain the pygmy dipole resonance, it is necessary but not sufficient to take into account the coupling of single-particle degrees of freedom to photon degrees of freedom. The results of the calculations performed for the first time for the isovector pygmy dipole resonance and the isovector electric giant dipole resonance in ¹²⁴Sn within a self-consistent approach involving, in addition to the standard quasiparticle random-phase approximation, a single-particle continuum and quasiparticle-phonon coupling of single-particle degrees of freedom to phonon degrees of freedom are presented. The results are found to be in satisfactory agreement with experimental data. The calculation of the isoscalar strength function in the energy region of the pygmy dipole resonance revealed that the nuclear-structure mechanism does not provide the isoscalar-strength suppression observed at energies in excess of 7 MeV in (α, α′γ) reactions; therefore, this suppression may stem from the reaction mechanism.     

Quasiparticles in a strongly correlated liquid with the fermion condensate: applications to high-temperature superconductors

A model of a strongly correlated electron liquid based on fermion condensation (FC) is extended to high-temperature superconductors. Within our model, the appearance of FC presents a boundary separating the region of a strongly interacting electron liquid from the region of a strongly correlated electron liquid. We study the superconductivity of a strongly correlated liquid and show that, under certain conditions, the superconductivity vanishes at temperatures T > T _c ≈ T _node, with the superconducting gap being smoothly transformed into a pseudogap. As a result, the pseudogap occupies only a part of the Fermi surface. The gapped area shrinks with increasing the temperature and vanishes at T = _T*. The single-particle excitation width is also studied. The quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by the effective masses and, intersecting near the binding energy that is on the order of the superconducting gap. It is argued that this strong change of the quasiparticle dispersion upon binding can be enhanced in underdoped samples because of strengthening the FC influence. The FC phase transition in the presence of the superconductivity is examined, and it is shown that this phase transition can be considered as driven by the kinetic energy.