Self-consistent Ladder Approximation Research Articles

Nambu-covariant many-body theory II: Self-consistent approximations

The theory of Self-Consistent Green’s Function (SCGF) is reformulated in an explicit Nambu-covariant fashion for applications to many-body systems at non-zero temperature in symmetry-broken phases. This is achieved by extending the Nambu-covariant formulation of perturbation theory, presented in the first part of this work, to non-perturbative schemes based on self-consistently dressed propagators and vertices. We work out in detail the self-consistent ladder approximation, motivated by a trade-off between numerical complexity and many-body phenomenology. Taking a complex general Hartree–Fock-Bogoliubov (HFB) propagator as a starting point, we also formulate and prove a sufficient condition on the stability of the HFB self-energy to ensure the convergence of the initial series of ladders at any energy. The self-consistent ladder approximation is written purely in terms of spectral functions and the resulting set of equations, when expressed in terms of Nambu tensors, are remarkably similar to those in the symmetry-conserving case. This puts the application of the self-consistent ladder approximation to symmetry-broken phases of infinite nuclear matter within reach.

Large enhancement of Edelstein effect in Weyl semimetals from Fermi-arc surface states

One remarkable feature of Weyl semimetals is the manifestation of their topological nature in the form of the Fermi-arc surface states. In a recent calculation by \cite{Johansson2018}, the current-induced spin polarization or Edelstein effect has been predicted, within the semiclassical Boltzmann theory, to be strongly amplified in a Weyl semimetal TaAs due to the existence of the Fermi arcs. Motivated by this result, we calculate the Edelstein response of an effective model for an inversion-symmetry-breaking Weyl semimetal in the presence of an interface using linear response theory. The scatterings from scalar impurities are included and the vertex corrections are computed within the self-consistent ladder approximation. At chemical potentials close to the Weyl points, we find the surface states have a much stronger response near the interface than the bulk states by about one to two orders of magnitude. At higher chemical potentials, the surface states' response near the interface decreases to be about the same order of magnitude as the bulk states' response. We attribute this phenomenon to the decoupling between the Fermi arc states and bulk states at energies close to the Weyl points. The surface states which are effectively dispersing like a one-dimensional chiral fermion become nearly nondissipative. This leads to a large surface vertex correction and, hence, a strong enhancement of the surface states' Edelstein response.

Hard-core boson approach to thespin−12triangular-lattice antiferromagnetCs2CuCl4at finite temperatures in magnetic fields higher than the saturation field

We study the high magnetic field regime of the antiferromagnetic insulator ${\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}$ by expressing the spin-1/2 operators in the relevant Heisenberg model in terms of hard-core bosons and implementing the hard-core constraint via an infinite on-site interaction. We focus on the case where the external magnetic field exceeds the saturation field ${B}_{c}\ensuremath{\approx}8.5\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ and is oriented along the crystallographic $a$ axis perpendicular to the lattice plane. Because in this case the excited states are separated by an energy gap from the ground state, we may use the self-consistent ladder approximation to take the strong correlations due to the hard-core constraint into account. In ${\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}$, there are additional interactions besides the hard-core interaction which we treat in self-consistent Hartree-Fock approximation. We calculate the spectral function of the hard-core bosons from which we obtain the in-plane components of the dynamic structure factor, the magnetic susceptibility, and the specific heat. Our results for the specific heat are in good agreement with the available experimental data. We conclude that the self-consistent ladder approximation in combination with a self-consistent Hartree-Fock decoupling of the non-hard-core interactions gives an accurate description of the physical properties of gapped hard-core bosons in two dimensions at finite temperatures.

Many-body effects in magnetic inelastic electron tunneling spectroscopy

Magnetic inelastic electron tunneling spectroscopy (IETS) shows sharp increases in conductance when a new conductance channel associated to a change in magnetic structure is open. Typically, the magnetic moment carried by an adsorbate can be changed by collision with a tunneling electron; in this process the spin of the electron can flip or not. A previous one-electron theory [Phys. Rev. Lett. {\bf 103}, 176601 (2009)] successfully explained both the conductance thresholds and the magnitude of the conductance variation. The elastic spin flip of conduction electrons by a magnetic impurity leads to the well known Kondo effect. In the present work, we compare the theoretical predictions for inelastic magnetic tunneling obtained with a one-electron approach and with a many-body theory including Kondo-like phenomena. We apply our theories to a singlet-triplet transition model system that contains most of the characteristics revealed in magnetic IETS. We use two self-consistent treatments (non-crossing approximation and self-consistent ladder approximation). We show that, although the one-electron limit is properly recovered, new intrinsic many-body features appear. In particular, sharp peaks appear close to the inelastic thresholds; these are not localized exactly at thresholds and could influence the determination of magnetic structures from IETS experiments.Analysis of the evolution with temperature reveals that these many-body features involve an energy scale different from that of the usual Kondo peaks. Indeed, the many-body features perdure at temperatures much larger than the one given by the Kondo energy scale of the system.

Vertex correction and Ward identity in U(1) gauge theory with a Fermi surface

We show that introduction of vertex corrections in the fully self-consistent ladder approximation does not modify dynamics of spinons and gauge fluctuations in the U(1) gauge theory with Fermi surface.

Theory of Ultrasonic Dispersion in Local Phonon Systems Coupled with Conduction Electrons

The physical origin of frequency dependence in elastic constants, which are often found in an ultrasound propagation in filled skutterudites and clathrate compounds, is investigated theoretically. This dependence arises from a coupling between the acoustic phonon and some optical phonons, which strongly interact with electrons. Using a self-consistent ladder approximation together with a pseudofermion mapping of the phonon to the single site Holstein Anderson model, a soft mode of the optical phonon at zero frequency is shown to emerge. The temperature dependence of the spectral weight of this soft mode shows an activation-type behavior, which is characterized by the optical phonon frequency. These features can generate the frequency dependence and the shoulder in the elastic constants observed in some filled skutterudites and clathrate compounds.

Role of bound pairs in the optical properties of highly excited semiconductors: A self-consistent ladder approximation approach

Presence of bound pairs (excitons) in a low-temperature electron-hole plasma is accounted for by including correlation between fermions at the ladder level. Using a simplified one-dimensional model with on-site Coulomb interaction, we calculate the one-particle self-energies, chemical potential, and optical response. The results are compared to those obtained in the Born approximation, which does not account for bound pairs. In the self-consistent ladder approximation the self-energy and spectral function show a characteristic correlation peak at the exciton energy for low temperature and density. In this regime the Born approximation overestimates the chemical potential. Provided the appropriate vertex correction in the interaction with the photon is included, both ladder and Born approximations reproduce the excitonic and free pair optical absorption at low density, and the disappearance of the exciton absorption peak at larger density. However, lineshapes and energy shifts with density of the absorption and photoluminescence peaks are drastically different. In particular, the photoluminescence emission peak is much more stable in the ladder approximation. At low temperature and density a sizeable optical gain is produced in both approximations just below the excitonic peak, however this gain shows unphysical features in the Born approximation. We conclude that at low density and temperature it is fundamental to take into account the existence of bound pairs in the electron-hole plasma for the calculation of its optical and thermodynamic properties. Other approximations that fail to do so are intrinsically unphysical in this regime, and for example are not suitable to address the problem of excitonic lasing.

One-Dimensional Model of Many-Exciton Effects in Photoluminescence Spectra

We solve numerically in one dimension and in the self-consistent ladder approximation the many-body problem of interacting electrons and holes. The model contains the minimal ingredients allowing to take into account the coexistence of a population of bound excitonic states with weakly correlated e-h pairs. A simplified contact potential for the Coulomb interaction is used. The strong e-h correlation leads to asymmetric single particle spectral functions with structures related to bound excitonic states. This asymmetry becomes more pronounced at low temperature when the formation of a dense exciton gas occurs. We discuss the role of the many-exciton effects by comparing the photoluminescence peak energies obtained in the ladder and Hartree-Fock approximation.

THE ATTRACTIVE HUBBARD MODEL IN 2-D : IS IT CAPABLE OF DESCRIBING A PSEUDOGAP AND PREFORMED PAIRS?

Deviations from Fermi liquid behavior are well documented in the normal state ofthe cuprate superconductors, and some of these differences seem to be related topretransitional features appearing at temperatures above T c. The observationof a pseudogap, e.g., in ARPES experiments, is a familiar example of this physics. Onepotential explanation for this behavior involves preformed pairs with finite lifetimesexisting in the normal state above T c. In this way, two characteristictemperatures can be established. A higher one T* at which pairs begin toform and the actual T c at which a phase-coherent superconducting phaseis established. In order to test these ideas we have investigated the negative UHubbard model in two dimensions in the fully self-consistent ladder approximation atlow electron densities. In the non-self-consistent version of this theory the systemalways shows an instability toward Bose-condensation of infinite lifetime pairs. In contrastto this, pairs obtain a finite lifetime due to pair–pair interaction and thesharp two-particle bound state is strongly lifetime broadened when self-consistency isapplied. A quasiparticle scattering rate which varies linearly with temperature is alsofound. The fully self-consistent calculation we were able to perform employed ak →-averaged approximation in which the self-energyloses its k →-dispersion due to ak →-average. This approximation is found to preservethe essential physics.

A Multiple Scattering Theory for a Magnetic Impurity Coupled to Quantum Antiferromagnets in Quasi-Two Dimensions

We study a magnetic impurity coupled to quantum antiferromagnets in quasi-two dimensions on the basis of the pseudofermion representation for the impurity spin. The dynamical impurity spin-correlation function and the impurity susceptibility are calculated. In the Néel phase, we use the self-consistent Born approximation in addition to the spin-wave expansion for the spins in the plane. In the paramagnetic phase, we consider the leading order in the 1/ N expansion (the self-consistent ladder approximation) in addition to the Schwinger-boson-mean-field theory for the spins in the plane. It is shown that the impurity susceptibility obeys the Curie law at high temperatures and converges to a finite value as T →0. Relations to the experiments on Nd 2- x Ce x CuO 4 are discussed.

Crystal field and Kondo effects in CeCu6 and CeAl3.

We calculate the temperature dependence of the specific heat, susceptibility, and resistivity for an isolated cerium ion in crystal-field environments appropriate for the cerium sites in ${\mathrm{CeCu}}_{6}$ and ${\mathrm{CeAl}}_{3}$. We use the self-consistent ladder approximation for intermediate and high temperatures and match to exact results to obtain low-temperature behavior. We find unusual temperature dependence for all the calculated quantities as a result of the competition between crystal-field effects and the Kondo effect. Our results for specific heat and susceptibility agree well with the data, except that the independent ion approximation predicts somewhat smaller Wilson ratios than observed, perhaps implying weak ferromagnetic correlations. The resistivity is not well reproduced.

Susceptibility of a Magnetic Impurity in Weakly Localized Regime

Interplay between the randomness and the s – d exchange interaction is investigated theoretically in the weakly localized regime through the temperature dependence of the susceptibility. In the first half the analytic calculations are performed perturbatively in terms of the s – d exchange coupling constant. It is shown that the quantum corrections to the susceptibility construct geometric series and can be summed up as simple formulae within the framework of the most divergent approximation. In the second half the numerical calculations are performed with the use of the self-consistent ladder approximation. It is shown that the effective Curie constant decreases more rapidly with decreasing the temperature than that in the usual Kondo systems.

Kondo Effect on Conductivity in Weakly Localized Regime

On the basis of the self-consistent ladder approximation, the Kondo effect in the weakly localized regime is investigated, particularly concerning the temperature dependence of the conductivity. It is shown that the conductivity in the disordered systems with a magnetic impurity decreases more rapidly by decreasing the temperature in the weakly localized regime through the interplay between the Anderson localization and the Kondo effect.

Thermopower in Ce Kondo Systems

The giant thermopower in metals with Ce 3+ impurities is theoretically studied. The relaxation time of a conduction electron is calculated as a function of energy in the selfconsistent ladder approximation by applying Abrikosov's pseudofermion technique to the Coqblin-Schrieffer exchange model with crystal field. The thermopower as well as the electrical resistivity exhibit universal behaviors if the crystal field is neglected. The crystal field induces the characteristic features and the anisotropy in the thermopower versus temperature curve. However, the sign of the thermopower is always positive in Ce system in contrast with Yb systems.

Effect of Crystal Field on Kondo Resistivity in Ce Compounds

The effect of crystal field on Kondo resistivity in metals with Ce impurities is theoretically studied. The T -matrix of conduction electron is calculated in the self-consistent ladder approximation by applying Abrikosov's pseudofermion technique to the Coqblin-Schrieffer exchange model. The numerical results of the resistivity in cubic and tetragonal crystals are compared with the experimental ones in Ce x La 1- x Al 2 and CeCu 2 Si 2 . Our theory provides a unified view of the magnetic and transport properties in Ce compounds and alloys.

Kondo effect on crystal field splitting

A theory is developed for the temperature dependence of crystal field energy levels of Ce ions in metals caused by the Kondo effect. Abrikosov’s pseudofermion technique is applied to the Coqblin–Schrieffer exchange model, and the self energy is derived in the self-consistent ladder approximation. The neutron quasi-elastic and inelastic scattering spectra are calculated in the system with cubic crystal field.