A. Sherman

Two-dimensional t-J model at moderate doping

Abstract:Using the method which retains the rotation symmetry of spin components in the paramagnetic state and has no preset magnetic ordering, spectral and magnetic properties of the two-dimensional t-J model in the normal state are investigated for the ranges of hole concentrations 0 ⩽ x ⩽ 0.16 and temperatures 0.01t ⩽ T ⩽ 0.2t. The used hopping t and exchange J parameters of the model correspond to hole-doped cuprates. The obtained solutions are homogeneous which indicates that stripes and other types of phase separation are not connected with the strong electron correlations described by the model. A series of nearly equidistant maxima in the hole spectral function calculated for low T and x is connected with hole vibrations in the region of the perturbed short-range antiferromagnetic order. The hole spectrum has a pseudogap in the vicinity of (0,π) and (π, 0). For x ≈ 0.05 the shape of the hole Fermi surface is transformed from four small ellipses around (±π/2,±π/2) to two large rhombuses centered at (0, 0) and (π,π). The calculated temperature and concentration dependencies of the spin correlation length and the magnetic susceptibility are close to those observed in cuprate perovskites. These results offer explanations for the observed scaling of the static uniform susceptibility and for the changes in the spin-lattice relaxation and spin-echo decay rates in terms of the temperature and doping variations in the spin excitation spectrum of the model.

The Mott transition in the strong coupling perturbation theory

Abstract Using the strong coupling diagram technique a self-consistent equation for the electron Green׳s function is derived for the repulsive Hubbard model. Terms of two lowest orders of the ratio of the bandwidth Δ to the Hubbard repulsion U are taken into account in the irreducible part of the Larkin equation. The obtained equation is shown to retain causality and reduces to Green׳s function of uncorrelated electrons in the limit U → 0 . Calculations were performed for the semi-elliptical initial band. It is shown that the approximation describes the Mott transition, which occurs at U c = 3 Δ / 2 . This value coincides with that obtained in the Hubbard-III approximation. At half-filling, for 0 U U c the imaginary part of the self-energy is nonzero at the Fermi level, which indicates that the obtained solution is not a Fermi liquid. At small deviations from half-filling the density of states shifts along the frequency axis without perceptible changes in its shape. For larger deviations the density of states is modified: it is redistributed in favor of the subband, in which the Fermi level is located, and for U > U c the Mott gap disappears.

Magnetic phase diagram of the spin-1 two-dimensional J1–J3 Heisenberg model on a triangular lattice

Abstract The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest, J 1 = − ( 1 − p ) J , J > 0 , and antiferromagnetic third-nearest-neighbor, J 3 = p J , exchange interactions is studied for 0 ≤ p ≤ 1 . Moriʼs projection operator technique is used. At p ≈ 0.2 the ground state is transformed from the ferromagnet into a disordered state, which is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector Q = Q ′ ≈ ( 1.16 , 0 ) at p ≈ 0.31 . With increasing p the ordering vector moves along the line Q ′ − Q c to the commensurate point Q c = ( 2 π 3 , 0 ) , which is reached at p = 1 . The final state can be conceived as four interpenetrating sublattices with the 120° spin structure on each of them. We apply the results to NiGa2S4.

Effective Hamiltonian and properties of the normal and superconducting phases of n-type cuprates

An effective low-energy Hamiltonian is derived from a microscopic multiband p-d model in the regime of strong electron correlations. The parameters of the p-d model are determined by comparison with the ARPES data for undoped Nd2CuO4. The Hamiltonian is the t-J* model in which hopping and exchange slowly decay with distance and are taken into account up to the fifth coordination sphere. The quasiparticle band structure is calculated as a function of the doping concentration with regard to short-range magnetic order, and the superconductivity theory with the spin-fluctuation pairing mechanism is constructed. Assuming that the parameters of the model do not depend on the doping level, we obtained quantitative agreement with the properties observed experimentally for the normal and superconducting phases without introducing fitting parameters.

The Hubbard model in the strong coupling theory at arbitrary filling

Equations for the electron Greens function of the two-dimensional Hubbard model, derived using the strong coupling diagram technique, are self-consistently solved for different electron concentrations n and tight-binding dispersions. Comparison of spectral functions calculated for the ratio of Hubbard repulsion to the nearest neighbor hopping with Monte Carlo data shows not only qualitative, but in some cases quantitative agreement in position of maxima. General spectral shapes, their evolution with momentum and filling in the wide range are also similar. At half-filling and for the next nearest neighbor hopping constant the Mott transition occurs at , where is the initial bandwidth. This value is close to those obtained in the cases of the semi-elliptical density of states and for . In the case and the Mott gap reaches maximum width at , and it is larger than that at for half-filling. In all considered cases positions of spectral maxima are close to those in the Hubbard-I approximation.

Incommensurate magnetic response in cuprate perovskites

Abstract The incommensurate magnetic response of the normal-state cuprate perovskites is interpreted based on Moris memory function approach and the t – J model of Cu–O planes. In agreement with experiment the calculated dispersion of the susceptibility maxima has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at ( 1 2 , 1 2 ± δ ) , ( 1 2 ± δ , 1 2 ) and at ( 1 2 ± δ , 1 2 ± δ ) , ( 1 2 ± δ , 1 2 ∓ δ ) in the lower and upper parabolas, respectively. The upper parabola reflects the dispersion of magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots.

Magnetic properties of the two-dimensional Heisenberg model on a triangular lattice

Abstract The spin Greens function of the antiferromagnetic Heisenberg model on a triangular lattice is calculated using Moris projection operator technique. At T = 0 the spin excitation spectrum is shown to have gaps at the wave vectors of the classical Neel ordering. This points to the absence of the antiferromagnetic long-range order in the ground state. The calculated spin correlation on the neighboring sites of the same sublattice is in good agreement with the value derived from exact diagonalization. The temperature dependencies of the spin correlations and the gaps are calculated.

Spin and charge fluctuations in the Hubbard model

Abstract Using the strong coupling diagram technique for calculating the electron Greens function of the two-dimensional Hubbard model we have summed infinite sequences of ladder diagrams, which describe interactions of electrons with spin and charge fluctuations. For sufficiently low temperatures and doping a pronounced four-band structure is observed in spectral functions. Its appearance is related to the proximity of the transition to the long-range antiferromagnetic order.

Continuum of many-particle states near the metal-insulator transition in the Hubbard model

Abstract The strong coupling diagram technique is used for investigating states near the metal-insulator transition in the half-filled two-dimensional repulsive Hubbard model. The nonlocal third-order term is included in the irreducible part along with local terms of lower orders. Derived equations for the electron Green’s function are solved by iteration for moderate Hubbard repulsions and temperatures. Starting iteration from Green’s functions of the Hubbard-I approximation with various distances of poles from the real frequency axis continua of different metallic and insulating solutions are obtained. The insulating solutions vary in the width of the Mott gap, while the metallic solutions differ in the shape of the spectral function in the vicinity of the Fermi level. Besides, different scenarios of the metal-insulator transition – with a sudden onset of a band of mobile states near the Fermi level and with gradual closure of the Mott gap – are observed with a change in temperature. In spite of these dissimilarities, all solutions have a common curve separating metallic and insulating states in the phase diagram. Near this curve metallic and insulating solutions coexist. For moderate Hubbard repulsions metallic solutions are not Fermi liquids.

Strongly correlated electron system in the magnetic field

Abstract In the range of hole concentrations 0.08 x 0.18 the density of states of the two-dimensional t – J model reveals oscillations with changing the magnetic field. Oscillation frequencies correspond to large Fermi surfaces. However, the oscillations are modulated with a frequency which is smaller by an order of magnitude. The modulation is related to van Hove singularities in the Landau subbands, which traverse the Fermi level with changing the field. The singularities are connected with bending the subbands due to strong electron correlations. The frequency of the modulation is of the same order of magnitude as quantum oscillation frequencies in underdoped cuprates.