A Different Theoretical Approach to the Spin Polaron Problem

Using the finite temperature (Matsubara) Green's function method, the spin polaron problem is investigated in the strong and weak coupling limits. The holon entropy and specific heat are calculated from the thermodynamic potential in the linked-cluster expansion method.     

Calculation of Entropy and Specific Heat in the Spin Polaron Formulation at Finite Temperature

Entropy and specific heat are calculated using the spin polaron formulation at finite temperature. Our theoretical approach makes use of the Matsubara Green's function method where the interaction term in the S-matrix is the spin polaron Hamiltonian, which is constructed in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. In the absence of this interaction term, the normal entropy and specific heat are obtained from the free holon thermodynamic potential and are found to resemble the BCS expressions in the low temperature regime. A second cumulant expansion of the thermodynamic potential with the spin polaron interaction yields an expression for the specific heat whose dominant term in the low temperature limit and small quasiparticle energy difference, resembles the superconducting-state electronic specific heat of the BCS theory.     

The Coulomb interaction in the generalized Hartree-Fock theory of superconductivity

The matrix self-energy equations of the generalized Hartree-Fock (GHF) theory of HTSC are reevaluated and rederived, while avoiding some shortcomings of the former derivation. The density of states is given for an interacted and renormalized electronic system. The self-energy equations are essentially different in several respects from the conventional Eliashberg equations. The matrix self-energy is analyzed with respect to its dependence on (p). It is found to depend one very weakly, which results in self-energy equations which depend on a single variable,, as in the conventional theory. However, it is found that the bare Coulomb interaction contributes extra terms to the pairing self-energy and to the renormalization function. In the simplified version of the equations, the effect of these two extra terms is incorporated as a single extra term of the renormalization function.     

The generalized Hartree-Fock theory of nonmagnetic high-temperature superconductors

The Eliashberg equations are generalized to apply to high-temperature superconductors without spin correlations. The generalization assumes any general electronic density of states. Consequently, it treats the Coulomb interaction dynamically, and takes into account the averaged momentum dependence of the self-energy and of the interactions. Unlike in the conventional Eliashberg equation, the bare Coulomb interaction yields a frequency-independent term in the renormalization function. This term breaks the symmetry of the self-energy, and changes the renormalization.     

Study of Hole Pair Condensation based on the SU(2) Slave-Boson Approach to the t-J Hamiltonian; Temperature, Momentum and Doping Dependences of Spectral Functions

Based on the U(1) and SU(2) slave-boson approaches to the t-J Hamil-tonian, we evaluate the one electron spectral functions for the hole doped high T _c cuprates for comparison with the angle resolved photoemission spectroscopy(ARPES) data. We find that the observed quasiparticle peak in the superconducting state is correlated with the hump which exists in the normal state. We find that the spectral weight of the quasiparticle peak increases as doping rate increases, which is consistent with observation. As a conse-quence of the phase fluctuation effects of the spinon and holon pairing order parameters the spectral weight of the predicted peak obtained from the SU(2) theory is found to be smaller than the one predicted from U(1) mean field theory.     

Selective Raman Scattering Detection of the Dirac Node and the Anti-node of the Spin Density Wave Gap and Magnetic Excitations in BaFe2As2

The electronic and magnetic excitations at the spin density wave (SDW) transition are investigated by Raman scattering. The multi-orbital electronic states induce the Dirac nodes in the SDW gap. The excitations near the nodes and anti-nodes are separately detected in accordance with the two-orbital tight-binding model. The exchange interactions are found to be given by the second derivative of the total energy with respect to the angle of the moment from two-magnon scattering. The two-magnon peak has the large spectral weight above twice the maximum energy of magnon. It is interpreted by the magnetic self-energy of the electron spectral function in the localized spin model or particle-hole excitations in the itinerant spin model.     

A Functional Generalization of the Field-Theoretical Renormalization Group Approach for the Single-Impurity Anderson Model

We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta et al. (in Phys. Rev. Lett. 85:4940, 2000), which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green’s function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which fully treat the interplay of particle-particle and particle-hole parquet diagrams and the effect of the two-loop self-energy feedback into them. We show that our results correctly reproduce accurate numerical renormalization group data for weak to slightly moderate interactions. These results are in excellent agreement with other functional Wilsonian RG works available in the literature. Since the field-theoretical RG method turns out to be easier to implement at higher loops than the Wilsonian approach, higher-order calculations within the present approach could improve further the results for this model at stronger couplings. We argue that the present RG scheme could thus offer a possible alternative to other functional RG methods to describe electronic correlations within this model.     

Spontaneously Broken Matsubara’s Time Invariance in Fermionic System: Macroscopic Quantum Ordered State of Matter

Spontaneous break down of translational invariance along the Matsubara time axis in a fermionic system is predicted and investigated using an exactly solvable model in analytical form. The broken symmetry state possesses discrete translational invariance along the Matsubara time axis and is characterized by the quantum order parameter (QOP) formed by condensed collective bosonic degrees of freedom of interacting fermions. The QOP’s Green’s function is finite and periodic along the Matsubara axis, but Wick-rotated to the axis of real frequencies it reveals a periodic “chain” of second order poles. Hence, QOP is not dissipative and, therefore, is “invisible” having a zero scattering cross section. Despite this, QOP changes measurable fermionic properties: instead of Landau quasi-particles with Fermi-velocity, there appear light-mass coherent fermionic states in the narrow vicinity of the Fermi-level, surrounded with overdamped states region (“pseudo-gap”) of a width proportional to QOP amplitude. Relevance of the picture to high-T _c “hidden order” and pseudo-gap state is discussed.     

Electron-Phonon vs. Electron-Impurity Interactions with Small Electron Bandwidths

It is a common practice to try to understand electron interactions in metals by defining a hierarchy of energy scales. Very often, the Fermi energy is considered the largest, so much so that frequently bandwidths are approximated as infinite. The reasoning is that attention should properly be focused on energy levels near the Fermi level, and details of the bands well away from the Fermi level are unimportant. However, a finite bandwidth can play an important role for low frequency properties: following a number of recent papers, we examine electron–impurity and electron–phonon interactions in bands with finite widths. In particular, we examine the behavior of the electron self-energy, spectral function, density of states, and dispersion, when the phonon spectral function is treated realistically as a broad Lorentzian function. With this phonon spectrum, impurity scattering has a significant nonlinear effect. PACS Numbers: 71.10.Ay, 71.20.-b, 63.20.Kr, 72.10.Fk Note that in the present paper we will restrict ourselves to situations with particle–hole symmetry, so that the bandwidth is twice the Fermi energy and the Fermi level lies precisely in between     

Thermodynamics and Single Particle Spectra of the Kondo Insulator by the Variational Self-Energy Method

The variational self-energy method is applied to a study of the half-filled periodic Anderson model. Trial-self-energies and the numerical value of the Luttinger–Ward functional are obtained by diagonalization of a single c – f dimer. The dependence of the zero-temperature single-particle gap on the c – f-hybridization is found in qualitative agreement with mean-field theory for the Kondo-lattice, the specific heat agrees well with numerical results from density-matrix-renormalization group calculations. The single particle spectral function at finite-temperature shows marked deviations from a hybridization picture which agree well with quantum Monte–Carlo results.     

Effect of spin fluctuations on electron self-energy

We consider the effect of spin fluctuations on the electron effective mass in the paramagnetic region just above the ferromagnetic transition of a magnetic lattice. For the spin fluctuations we use a now standard hydrodynamic model with an attendant large temperature dependence in the spin fluctuation spectral density, which increases rapidly as the transition is approached from above. This has significant effects on the self-energy, which could be measured in normal-state tunneling.     

Charge Excitations in Two-Leg Ladders: A tDMRG Approach

We study the dynamics of holon–doublon pairs in two-leg Hubbard ladders with the time-dependent Density Matrix Renormalization-Group approach. Benchmark results show that the Krylov algorithm is well suited to calculate the time dependence of observables in these systems. Furthermore, we show that the dynamics of the holon–doublon depend strongly on the coupling asymmetry within the ladder, indicating that the ladder geometry plays a role in the decay of these elementary charge excitations.     

A Structure Function Representation Theorem with Applications to Frequency Stability Estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. The theorem proved here allows one to obtain the structure function (covariances of the nth differences) of such a process in terms of the differences of a single function of one time variable. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability.     

Josephson Tunneling Current in Spin Polaron Theory

Using an effective Hamiltonian derived from spin polaron theory, the Josephson tunneling current between two high temperature superconductors is calculated. The method makes use of the Matsubara Green??s function and a canonical transformation analogous to the Schrieffer?CWolff transformation. The Josephson tunneling current is then obtained in terms of the energy gap function and the tunneling matrix, and it was found to have some similarities with the BCS result.     

A dyson equation approach to the calculation of correlation functions

We derive an integral equation for the linear response of a Fermi liquid which is the analog of Dyson's equation for the one-particle Green's function. The corresponding particle-hole self-energy depends only on the frequency and the wave number of the applied field, and we are able to give an explicit expression for it. The solution of the response function resembles ordinary RPA, only the bare interaction is replaced by this self-energy. Current approximations are easily rederived within our technique. Criteria to get approximations which conserve particle number, momentum, and energy are equivalent to those of Kadanoff and Baym.     

First-principles approach to the calculation of electronic spectra in clusters

We discuss a method for first-principles calculations of photoemission spectra in small clusters, going well beyond a standard density functional theory-local density approximation (DFT-LDA) approach. Starting with a DFT-LDA calculation, we evaluate self-energy contributions to the quasiparticle energies of an electron or hole in the GW scheme, where the self-energy Σ = GW is constructed from the one-particle Green's function G and the RPA screened Coulomb interaction W. The contributions of structural relaxation are taken into account. We show the importance of these effects at the example of the photoemission spectrum of SiH₄. We also briefly discuss results for longer hydrogenated silicon chains, and address the problem of optical absorption.     

Blood oxygenation measurements by multichannel reflectometry on the venous and arterial structures of the retina

The aim of the present study was to propose a model and a method to derive the oxyhemoglobin blood content in the retinal veins and arteries by full spectrum reflectometry measurements in the spectral zone from 430 to 680?nm. We proposed a mathematical equation expressed as a linear combination of two terms S(OHb)(λ) and S(Hb)(λ) representing the normalized spectral absorption functions of the hemoglobin and the oxyhemoglobin, one term λ(-n) representing the ocular media absorption with scattering, and a family of multi-Gaussian functions, which usefully compensate for the noncompatibility of the model and the experimental data in the red spectral zone. The present paper suggests that the spectral reflection function in the area from 520 to 580?nm is optimal in calculating the oxyhemoglobin concentration of the blood contained in the endothelial structures of retinal vessels. The model calculation needs a function (1/λ)(-n) that corrects for the ocular media absorption and light scattering on the vessels' structures. For the spectral area of lights with wavelength larger than 580?nm, the reflected light represents mainly the light scattering on the red blood cells.