Coupling of electrons and phonons in a doped antiferromagnet

It is well-known that low-energy electronic excitations in high-T _c superconductors have energies of the order of the exchange couplingJ, i.e. of the same order as the phonon energies. Therefore, low-energy electronic excitations and phonons should strongly influence each other. To investigate this problem we consider a coupled electron-phonon system. For the electronic degrees of freedom we start from the three band Hubbard or Emery model. In analogy to the transformation of the three band Hubbard model to thet?J model, studied by Zhang and Rice, we derive an effective electron-phonon interaction. Its electronic degrees of freedom are those of thet?J model which couple to the phonons of the original system. The coupling of electrons and phonons is discussed by means of the phonon Green function for a breathing-like mode.     

d-Wave superconductivity from correlated-hopping interactions determined by angle-resolved photoemission spectroscopy

Starting from a generalized Hubbard model with correlated-hopping interactions, we solve numerically two coupled integral equations within the Bardeen–Cooper–Schrieffer formalism, in order to study the doping effects on the critical temperature (_Tc$T_c$), d-wave superconducting gap, and the electronic specific heat. Within the mean-field approximation, we determine the single- and correlated-electron-hopping parameters for La_2 − xSr_xCuO₄ by using angle-resolved photoemission spectroscopy data. The resulting parametrized Hubbard model is able to explain the experimental _Tc$T_c$ variation with the doping level (x). Moreover, the observed power-law behavior of the superconducting specific heat is reproduced by this correlated-hopping Hubbard model without adjustable parameters.     

Band structure and antiferromagnetism of a single CuO2 layer

We have solved a set of self-consistency equations for the three-band model describing electrons coupled strongly by antiferromagnetic correlations in a single CuO₂ layer. Strong but finite Hubbard correlations are taken into account by using a random phase approximation for the electronic propagators which contain the combined effect of both the Hubbard correlation and the hybridization of copper and nearest neighbor oxygen states. From the Green functions the band structure is determined, which depends strongly on the doping fraction and the antiferromagnetic order parameter 〈s_Q〉. The main impact of doping is to decrease the magnitude of antiferromagnetic fluctuations, although the decrease appears to be quite slow when compared with experimental data.     

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

A microscopic theory of superconductivity is considered in the framework of the Hubbard p-d model for the CuO₂ plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t-J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments.     

Kinks and waterfalls in the dispersion of ARPES features

In this paper we use a generic form for the Green function G(k, ω) in a correlated metal, already proven successful in describing ARPES line shapes [1]. The associated many body self-energy function has only a single pole. We now investigate, whether this generic model can be used all the way to the limit of strong correlations and, when applied to ARPES intensities, whether it is able to explain some of the ubiquitous dispersive crossover phenomena that have been attributed to dynamical, i.e.: ω-dependent effects. We argue that a quantitative interpretation of experimental data requires to calculate extrema not only in the momentum distribution curve but also in the energy distribution curve. In passing, we give a formula for the extrema in the latter distribution that is valid for the general G(k, ω) in a many body system. To our knowledge, this is a new formula, not found in the literature. The investigation of the generic model proceeds on two levels: on the one hand, we explore the rich variety of crossovers that can be predicted and linked to well defined features in the complex ω-plain. On the other hand, we show that the generic one-pole self-energy can be viewed as a projection on the low energy sector of a microscopic solution, belonging to a lattice model of interacting fermions. To obtain approximate microscopic solutions, we use our continued fraction method [2] and [3]. As an explicit example, we study the projection for the case of a hole doped Hubbard model in infinite dimension. A discussion section gives examples, how the generic model is able to cope with the ubiquity of the crossover phenomena, also in finite dimension and beyond the Hubbard model.     

The su(n) Hubbard model

The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I introduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that makes it the natural su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the transfer matrix commutes with the Hamiltonian. While the model is integrable in one dimension, it provides a generalization of the Hubbard Hamiltonian in any dimension.     

The matrix product ansatz for the six-vertex model

Recently it was shown that the eigenfunctions for the asymmetric exclusion problem and several of its generalizations as well as a huge family of quantum chains, like the anisotropic Heisenberg model, Fateev–Zamolodchikov model, Izergin–Korepin model, Sutherland model, t–J$t\text{–}J$ model, Hubbard model, etc, can be expressed by a matrix product ansatz. Differently from the coordinate Bethe ansatz, where the eigenvalues and eigenvectors are plane wave combinations, in this ansatz the components of the eigenfunctions are obtained through the algebraic properties of properly defined matrices. In this work, we introduce a formulation of a matrix product ansatz for the six-vertex model with periodic boundary condition, which is the paradigmatic example of integrability in two dimensions. Remarkably, our studies of the six-vertex model are in agreement with the conjecture that all models exactly solved by the Bethe ansatz can also be solved by an appropriated matrix product ansatz.     

First-principles calculation of the energy of compressed calcium

The energy of a calcium crystal with a simple cubic lattice as a function of the ratio (t/U) between two internal parameters of the Hubbard model has been calculated using the Hubbard model for the s bands, equations of motion, and direct algebraic method. The electronic spectra have been calculated for the 4s band of the crystal in two principal symmetry directions of the first Brillouin zone. The calculations have been performed at temperatures T ₁ = 0 K and T ₂ = 1000 K. All calculations have been carried out for different interaction energies U of s electrons, one angle, and their different concentrations n in the range 0 ≤ n ≤ 2. The calculations have demonstrated that the dependences of the energy and electronic spectra in this compressed state are very smooth. The occupation of the Ca 4s band is in good agreement with the results of the pioneering calculations of compressed Ca (and a number of other metals), which were carried out by Gandel’man and his colleagues in the Wigner-Seitz spherical cell approximation. It has been shown that the performed analysis accurately reproduces the data obtained on the superconductivity in terms of the Bardeen-Cooper-Schrieffer theory if the 4s band is half-occupied.     

Optical conductivity in the t − J model

Frequency dependent conductivity σ(ω) is calculated for the t ? J model by applying the memory function technique in terms of the Hubbard operators. The relaxation rate due to electron scattering on spin and charge dynamical fluctuations is calculated and a generalized Drude law for σ(ω) is obtained. For a model with an incoherent spectrum for one-hole excitations we obtain a universal form for frequency dependence of relaxation rate and conductivity in terms of the scaling function γ(ω/kT). The relaxation rate for the t ? J model is quite different from that one for the conventional Hubbard model in the strong coupling limit where it vanishes due to an exact cancellation of the intraband scattering and virtual interband transitions.     

Algebraic Bethe ansatz for the one-dimensional Hubbard model with chemical potential

The integrability and the algebraic Bethe ansatz approach for the one-dimensional (1D) Hubbard model with chemical potential are studied in the framework of the quantum inverse scattering method. We also investigate the hidden local gauge invariance for the model. It is found that the R-matrix only permits Abelian $\text{U(1) ⋇}{}_{\mathrm{s}}\text{U(1)}$ gauge transformations, and it is shown that the energy spectrum is gauge invariant whereas the eigenvectors and the Bethe ansatz equations are explicitly gauge dependent.     

Superconductivity enhanced by d-density wave: A weak-coupling theory

Making a revision of mistakes in Ref. [19], we present a detailed study of the competition and interplay between the d-density wave (DDW) and d-wave superconductivity (DSC) within the fluctuation-exchange (FLEX) approximation for the two-dimensional (2D) Hubbard model. In order to stabilize the DDW state with respect to phase separation at lower dopings a small nearest-neighbor Coulomb repulsion is included within the Hartree-Fock approximation. We solve the coupled gap equations for the DDW, DSC, and π-pairing as the possible order parameters, which are caused by exchange of spin fluctuations, together with calculating the spin fluctuation pairing interaction self-consistently within the FLEX approximation. We show that even when nesting of the Fermi surface is perfect, as in a square lattice with only nearest-neighbor hopping, there is coexistence of DSC and DDW in a large region of dopings close to the quantum critical point (QCP) at which the DDW state vanishes. In particular, we find that in the presence of DDW order the superconducting transition temperature T_c can be much higher compared to pure superconductivity, since the pairing interaction is strongly enhanced due to the feedback effect on spin fluctuations of the DDW gap. π-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small. In the present work, we have developed a weak-coupling theory of the competition between DDW and DSC in 2D Hubbard model, using the static spin fluctuation obtained within FLEX approximation and ignoring the self-energy effect of spin fluctuations. For our model calculations in the weak-coupling limit we have taken U/t=3.4, since the antiferromagnetic instability occurs for higher values of U/t.     

Orthofermions versus Gutzwiller projection operator approach for the infinite U Hubbard model

A comparison of two well-known approaches for strongly correlated electron systems, namely, nested Bethe ansatz implemented through orthofermion algebra and Gutzwiller projection operator formalism, is made by calculating the energy spectrum of 1D infinite U Hubbard model for a finite system consisting of three particles on a four site anisotropic closed chain. It is shown that orthofermion algebra always leads to at least an eight hold degeneracy in the energy spectrum corresponding to all 2³ spin configurations, consistent with the nested Bethe ansatz solution leading to a N²-fold degeneracy of energy levels of an N electron system. Such a degeneracy is absent in the Gutzwiller projection operator approach. This finding shows the limitations of the Gutzwiller projection method and at the same time the relevance of orthofermion approach for the infinite U Hubbard model.     

Multi-leg integrable ladder models

We construct integrable spin chains with inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of coupled Yang–Baxter equations. This construction yields P-leg integrable ladder Hamiltonians. We analyse the corresponding quantum group symmetry and present algebraic Bethe ansatz (ABA) solution.     

On the solutions of the infinite U Hubbard model through orthofermions

We reinforce our earlier arguments for the soundness of the orthofermion approach to the infinite U Hubbard model by studying the distribution and the partition functions for a system of noninteracting orthofermions as well as for two systems of noninteracting orthofermions coupled through inter system single particle hopping.     

Kinematic spin-fluctuation mechanism of high-temperature superconductivity

We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands, there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electron kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators, which results in the kinematic spin-fluctuation pairing mechanism for V ? W. The theory is based on the Mori projection technique in the equation of motion method for the Green’s functions in terms of the Hubbard operators. The doping dependence of the superconductivity temperature T _c is calculated for various values of U and V.     

Effect of charge-spin separation on the conductance through interacting low-dimensional rings

We calculate the conductance through Aharonov-Bohm chain and ladder rings pierced by a magnetic flux which couples with the charge degrees of freedom. The system is weakly coupled to two leads and contains strongly interacting electrons modeled by the prototypical t-J and Hubbard models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation. We also show how the dips evolve when the parameters of the models depart from the ideal case of total spin-charge separation. The ladder ring can be mapped onto an effective model for large anisotropy which can be easily analyzed. These results open the possibility of observing this peculiar many-body phenomenon in anisotropic ladder systems and in real nanoscopic devices.     

Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any U>0 to U=∞ is also shown. We use this continuity property, combined with the proof that the norm of the wavefunction obtained with the generalized Bethe Ansatz is not zero, to prove that the solution gives us the ground state of the finite system, as assumed by Lieb and Wu. Lastly, for the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the Lieb-Wu solution of the 1D Hubbard model.     

The Renormalization Group Treatment of the Hubbard Model

The article presents the renormalization group treatment to the Hubbard model. To begin with, the bosonization of Hubbard model Hamiltonian is performed. We have obtained the sine-Gordon Hamiltonian. We have further approximated this Hamiltonian by the Hamiltonian of ⁴-theory. Then we utilized Wilson's results of the renormalization group method and obtained the recursion formula for the Hubbard model. Having solved these formulas we have obtained the critical indices for the Hubbard model.     

On the density of states for the Hubbard model: Pseudo-particle Keldysh diagram method—an alternative to DMFT?

It is shown how to construct Keldysh diagram technique for pseudo-particle approach to the Hubbard model. We propose self-consistent equations for pseudo particle and electron Green’s functions in Keldysh diagram technique. Nonlocal effects (spatial dispersion) are included in single impurity problem in this method. Thus we can get rid of the artificial central peak (of Kondo type) in the density of states which is inevitable in Dynamical Mean Field Theory (DMFT). The changes in the density of states for 2D Hubbard model due to variation of Coulomb repulsion U and electron concentration are analyzed.     

Some exact results for the Kondo lattice with infinite exchange interaction

Using an exact equivalence between the Kondo lattice with infinite J and the Hubbard model with infinite U, we show that the ground state of the Kondo lattice is non-magnetic for concentrations of conduction electrons close to 1, but there are still some magnetic regions even for J → ∞.