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We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $\mathrm{\ensuremath{\Gamma}}$ and isotropic third-nearest-neighbor interact ion ${J}_{3}$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ and ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$, and Ru-based materials such as $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate Hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is $\mathrm{\ensuremath{\Gamma}}=Kg0$, where $K$ is the Kitaev coupling. Within our approach, we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of nonlinear magnon coupling in interpreting broad features in the neutron-scattering spectra.

Motivated by the recent heat transport experiments in 2D antiferromagnets, such as La$_2$CuO$_4$, where the exchange coupling $J$ is larger than the Debye energy $\Theta_{\rm D}$, we discuss different types of relaxation processes for magnon heat current with a particular focus on coupling to 3D phonons. We study thermal conductivity by these in-plane magnetic excitations using two distinct techniques, Boltzmann formalism within the relaxation-time approximation and memory-function approach. Within these approaches, a close consideration is given to the scattering of magnons by both acoustic and optical branches of phonons. A remarkable accord between the two methods with regards to the asymptotic behavior of the effective relaxation rates is demonstrated. Additional scattering mechanisms, due to grain boundaries, impurities, and finite correlation length in the paramagnetic phase, are discussed and included in the calculations of the thermal conductivity $\kappa(T)$. Again, we demonstrate a close similarity of the results from the two techniques of calculating $\kappa(T)$. Our complementary approach strongly suggests that scattering from optical or zone-boundary phonons is important for magnon heat current relaxation in a high temperature window of $\Theta_D\lesssim T \ll J$., Comment: 21+ pages, 16 figures

The competition between long-range and short-range interactions among holes moving in an antiferromagnet (AF), is studied within a model derived from the spin density wave picture of layered transition metal oxides. A novel numerical approach is developed which allows one to solve the problem at finite hole densities in very large systems (of order hundreds of lattice spacings), albeit in a quasiclassical limit, and to correctly incorporate the long-range part of the Coulomb interaction. The focus is on the problem of charge ordering and the charge phase diagram: at low temperatures four different phases are found, depending on the strength of the magnetic (dipolar) interaction generated by the spin-wave exchange, and the density of holes. The four phases are the Wigner crystal, diagonal stripes, a grid phase (horizontal-vertical stripe loops) and a glassy-clumped phase. In the presence of both in-plane and out-of-plane charged impurities the stripe ordering is suppressed, although finite stripe segments persist. At finite temperatures multiscale (intermittency) dynamics is found, reminiscent of that in glasses. The dynamics of stripe melting and its implications for experiments is discussed., A number of minor changes; one figure removed; REVTEX

The t-J{sub z} model is the strongly anisotropic limit of the t-J model which captures some general properties of doped antiferromagnets (AF{close_quote}s). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single- and two-hole spectra with a high accuracy using a regular diagram technique combined with a real-space approach. At the same time, numerical studies of this model via exact diagonalization on small clusters show negligible finite-size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in {ital p}- and {ital d}-wave channels at realistic values of t/J. Interactions leading to pairing and effects selecting {ital p} and {ital d} waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic t-J-like model. Possible implications for preformed pairs formation and phase separation are drawn. {copyright} {ital 1999} {ital The American Physical Society}

We report on a detailed examination of numerical results and analytical calculations devoted to a study of two holes doped into a two-dimensional, square lattice described by the t-J model. Our exact diagonalization numerical results represent the first solution of the exact ground state of 2 holes in a 32-site lattice. Using this wave function, we have calculated several important correlation functions, notably the electron momentum distribution function and the hole-hole spatial correlation function. Further, by studying similar quantities on smaller lattices, we have managed to perform a finite-size scaling analysis. We have augmented this work by endeavouring to compare these results to the predictions of analytical work for two holes moving in an infinite lattice. This analysis relies on the canonical transformation approach formulated recently for the t-J model. From this comparison we find excellent correspondence between our numerical data and our analytical calculations. We believe that this agreement is an important step helping to justify the quasiparticle Hamiltonian, and in particular, the quasiparticle interactions, that result from the canonical transformation approach. Also, the analytical work allows us to critique the finite-size scaling ansatzes used in our analysis of the numerical data. One important feature that we can infer from this successful comparison involves the role of higher harmonics in the two-particle, d-wave symmetry bound state -- the conventional (\cos(k_x) - \cos(k_y)) term is only one of many important contributions to the d-wave symmetry pair wave function.

Dispersion relation for the Cu${\mathrm{O}}_{2}$ hole is calculated based on the generalized $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}J$ model, recently derived from the three-band one. Numerical ranges for all model parameters, $\frac{t}{J}=2.4\ensuremath{-}2.7$, $\frac{{t}^{\ensuremath{'}}}{t}=0.0 \mathrm{to} \ensuremath{-}0.25$, $\frac{{t}^{\ensuremath{'}\ensuremath{'}}}{t}=0.1\ensuremath{-}0.15$, and three-site terms $2{t}_{N}\ensuremath{\sim}{t}_{S}\ensuremath{\sim}\frac{J}{4}$ have been strongly justified previously. Physical reasons for their values are also discussed. A self-consistent Born approximation is used for the calculation of the hole dispersion. Good agreement between calculated ${E}_{\mathrm{k}}$ and one obtained from the angle-resolved photoemission experiments is found. A possible explanation of the broad peaks in the experimental energy distribution curves at the top of the hole band is presented.

We study high-field magnon dynamics and examine the dynamical structure factor in the quasi-two-dimensional tetragonal Heisenberg antiferromagnet with interlayer coupling corresponding to realistic materials. Within spin-wave theory, we show that a nonzero interlayer coupling mitigates singular corrections to the excitation spectrum occurring in the high-field regime that would otherwise require a self-consistent approach beyond the $1/S$ approximation. For the fields between the threshold for decays and saturation field, we observe widening of the two-magnon sidebands with significant shifting of the spectral weight away from the quasiparticle peak. We find spectrum broadening throughout large regions of the Brillouin zone, dramatic redistributions of spectral weight to the two-magnon continuum, two-peak structures, and other features clearly unlike conventional single-particle peaks.

The t-J-model effective hopping integral is determined from the three-band Hubbard model for the charge carriers in ${\mathrm{CuO}}_{2}$ planes. For this purpose the values of the superexchange constant J and the charge-transfer gap ${\mathit{E}}_{\mathrm{gap}}$ are calculated in the framework of the three-band model. The energies of the local states for added electron and hole are obtained from the systematic analytical reduction of the three-band model and their kinetic energy is found from the accurate variational approach using the t-J model. Fitting values of J and ${\mathit{E}}_{\mathrm{gap}}$ to the experimental data allows us to narrow the uncertainty region of the threeband model parameters. As a result, the t/J ratio of the t-J model is fixed in the range 2.4--2.7 for holes and 2.5--3.0 for electrons. This approach explains the formation of the Frenkel exciton and correctly describes the main features of the charge-transfer spectrum.

Dynamical properties of the square-lattice Heisenberg antiferromagnet in applied magnetic field are studied for arbitrary value S of the spin. Above the threshold field for two-particle decays, the standard spin-wave theory yields singular corrections to the excitation spectrum with logarithmic divergences for certain momenta. We develop a self-consistent approximation applicable for S >= 1, which avoids such singularities and provides regularized magnon decay rates. Results for the dynamical structure factor obtained in this approach are presented for S = 1 and S = 5/2., 12 pages, 11 figures, final version

The spin stiffness ${\ensuremath{\rho}}_{s}$ of a two-dimensional (2D) Heisenberg antiferromagnet depends nonanalytically on external magnetic field. We demonstrate that the hydrodynamic relation between ${\ensuremath{\rho}}_{s}$, the uniform susceptibility $\ensuremath{\chi}$, and the spin-wave velocity $c$ is not violated by such a behavior because similar nonanalytic terms from all three quantities mutually cancel out. In this work, explicit expressions for the field-dependent spin stiffness and for the magnon velocity of the 2D square-lattice antiferromagnet are obtained by direct calculation to order $1/S$ and in the whole range of magnetic fields.

We study the problem of heat transport in one-dimensional (1D) spin-chain systems weakly coupled to three-dimensional phonons and impurities. We consider the limit of fast spin excitations and slow phonons, applicable to a number of compounds of the cuprates family, such as Sr2CuO3, where the superexchange J is much larger than the Debye energy. In this case the Umklapp scattering among the spin excitations is strongly suppressed for all relevant temperatures. We argue that the leading scattering mechanism for the spin excitations at not too low temperatures is the "normal" (as opposed to the Umklapp) spin-phonon scattering in which the non-equilibrium momentum is transferred from the spin subsystem to phonons where it quickly relaxes through the "phonon bath". Because of the lower dimensionality of the spin excitations it is only the momentum along the chains which is conserved in such a scattering. We find that this effect leads to a particular momentum- and temperature-dependence of the spin-phonon relaxation rate valid for the broad class of low-dimensional spin systems. Subsequently we demonstrate that the spin-phonon relaxation mechanism is insufficient for the low-energy, long-wavelength 1D spin-chain excitations, which make the thermal conductivity diverge. We complete our consideration by taking into account the impurity scattering, which in 1D cuts off the quasi-ballistic spin excitations and renders the thermal conductivity finite. Our results compare very well with the existing experimental data for Sr2CuO3. Using our microscopic insight into the problem we propose further experiments and predict an unusual impurity concentration dependence for a number of quantities., 22 pages, 10 figures. Long story

Three well-known perturbative approaches to deriving low-energy effective theories, the degenerate Brillouin-Wigner perturbation theory (projection method), the canonical transformation, and the resolvent methods, are compared. We use the Hubbard model as an example to show how, to fourth order in hopping $t$, all methods lead to the same effective theory, namely the $t\text{\ensuremath{-}}J$ model with ring exchange and various correlated hoppings. We emphasize subtle technical difficulties that make such a derivation less trivial to carry out for orders higher than second. We also show that in higher orders, different approaches can lead to seemingly different forms for the low-energy Hamiltonian. All of these forms are equivalent since they are connected by an additional unitary transformation whose generator is given explicitly. The importance of transforming the operators is emphasized and the equivalence of their transformed structure within the different approaches is also demonstrated.

Recent first-principles calculations of the phonon dispersion curves in MgB2 have suggested the presence of anomalies in some of the curves, particularly in the longitudinal acoustical (LA) branch in the Gamma to A direction. Similar behavior has been observed in numerous other superconductors with T-c's higher than those of standard electron-phonon BCS superconductors. Phenomenological calculations of the Gamma-->A LA dispersion based on both an acoustical plasmon and a "resonant polarization" mechanism are given here to emphasize the importance of these similarities.

We have studied the static and dynamic magnetic properties of two-dimensional (2D) and quasi-two-dimensional, spin-S, quantum Heisenberg antiferromagnets (QHAF) diluted with spinless vacancies. Using spin-wave theory and T-matrix approximation we have calculated the staggered magnetization, M(x,T), the neutron scattering dynamical structure factor, S(k,omega), the 2D magnetic correlation length, \xi(x,T), and the Neel temperature, T_N(x), for the quasi-2D case. We find that in 2D the hydrodynamic description of excitations in terms of spin-waves breaks down at the wavelength larger than \ell/a ~ exp(\pi/4x), x being impurity concentration and "a" the lattice spacing. The density of states acquires a constant term and exhibits an anomalous peak at omega omega_0 associated with the low-energy localized excitations. These anomalies lead to a substantial enhancement of the magnetic specific heat, C_M, at low temperatures. Although the dynamical properties are significantly modified we show that 2D is not the lower critical dimension for this problem. Our results are in quantitative agreement with the recent Monte Carlo simulations and experimental data for S=1/2, S=1, and S=5/2., Comment: 24 pages, 15 figures, RevTeX. Some of the results presented here were briefly reported in our previous paper: cond-mat/0008412, PRL 87, 067209 (2001)