Derivation of effective spin models from a three band model for CuO_2-planes

The derivation of effective spin models describing the low energy magnetic properties of undoped CuO_2-planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi-band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La_2CuO_4. Starting from a conventional three-band model we determine the exchange couplings for the nearest and next-nearest neighbor Heisenberg exchange as well as for 4- and 6-spin exchange terms via a direct perturbation expansion up to 12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping t_pd. Our results demonstrate that this perturbation expansion does not converge for hopping parameters of the relevant size. Well behaved extrapolations of the couplings are derived, however, in terms of Pade approximants. In order to check the significance of these results from the direct perturbation expansion we employ the Zhang-Rice reformulation of the three band model in terms of hybridizing oxygen Wannier orbitals centered at copper ion sites. In the Wannier notation the perturbation expansion is reorganized by an exact treatment of the strong site-diagonal hybridization. The perturbation expansion with respect to the weak intersite hybridizations is calculated up to 4th order for the Heisenberg coupling and up to 6th order for the 4-spin coupling. It shows excellent convergence and the results are in agreement with the Pade approximants of the direct expansion. The relevance of the 4-spin coupling as the leading correction to the nearest neighbor Heisenberg model is emphasized.Comment: 27 pages, 10 figures. Changed from particle to hole notation, right value for the charge transfer gap used; this results in some changes in the figures and a higher value of the ring exchang

Modulational instability in asymmetric coupled wave functions

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the GVD terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.Comment: NEXT Sigma-Phi Statistical Physics Conference (2005, Kolymbari, Greece) Proceedings, submitted; v.2 is a shorter version of the text in v.1 (more detailed and somehow more explanatory, yet abbreviated due to submission regulations); some typos corrected as wel

Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunneling. The energy gap is never zero when the tunneling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalised phase from a self-trapping phase which occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Analytic expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.Comment: 12 pages, 5 .eps figures + 4 figs, classical analysis, perturbation theor

Macrospin approximation and quantum effects in models for magnetization reversal

The thermal activation of magnetization reversal in magnetic nanoparticles is controlled by the anisotropy-energy barrier. Using perturbation theory, exact diagonalization and stability analysis of the ferromagnetic spin-s Heisenberg model with coupling or single-site anisotropy, we study the effects of quantum fluctuations on the height of the energy barrier. Opposed to the classical case, there is no critical anisotropy strength discriminating between reversal via coherent rotation and via nucleation/domain-wall propagation. Quantum fluctuations are seen to lower the barrier depending on the anisotropy strength, dimensionality and system size and shape. In the weak-anisotropy limit, a macrospin model is shown to emerge as the effective low-energy theory where the microscopic spins are tightly aligned due to the ferromagnetic exchange. The calculation provides explicit expressions for the anisotropy parameter of the effective macrospin. We find a reduction of the anisotropy-energy barrier as compared to the classical high spin-s limit.Comment: 10 pages, 11 figure

Nonperturbative Light-Front QCD

In this work the determination of low-energy bound states in Quantum Chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve Quantum Electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero masses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling never leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, but with a coefficient that vanishes at the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the Constituent Quark Model with the complexities of Quantum Chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a formulation entails. We describe the renormalization process first using a qualitative phase space cell analysis, and we then set up a precise similarity renormalization scheme with cutoffs on constituent momenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that determines the artificial potential, with binding energies required to be fourth order in the coupling as in QED. Next there is a calculation of the leading radiative corrections to these masses, which requires our renormalization program. Then the real struggle of finding the right extensions to perturbation theory to study the strong-coupling behavior of bound states can begin.Comment: 56 pages (REVTEX), Report OSU-NT-94-28. (figures not included, available via anaonymous ftp from pacific.mps.ohio-state.edu in subdirectory pub/infolight/qcd