On the Incommensurate Phase in Modulated Heisenberg Chains

Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with sinusoidal modulation and incommensurate with solitonic modulation. We focus on the order of the phase transition from the commensurate dimerized phase (D) to the incommensurate phase (I). It is shown that the order of the phase transition depends sensitively on the model. For the solitonic model in particular, a $k$-dependent elastic energy modifies the order of the transition. Furthermore, we calculate gaps in the incommensurate phase in adiabatic approximation.Comment: 8 pages, 9 figure

Excitation Spectra of Structurally Dimerized and Spin-Peierls Chains in a Magnetic Field

The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields h < h_c1, an incommensurate regime (h_c1 < h < h_c2) in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin polarized phase above an upper critical field h_c2. For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.Comment: RevTex, 10 pages with 8 eps figure

Incompatibility of modulated checkerboard patterns with the neutron scattering resonance peak in cuprate superconductors

Checkerboard patterns have been proposed in order to explain STM experiments on the cuprates BSCCO and Na-CCOC. However the presence of these patterns has not been confirmed by a bulk probe such as neutron scattering. In particular, simple checkerboard patterns are inconsistent with neutron scattering data, in that they have low energy incommsensurate (IC) spin peaks rotated 45 degrees from the direction of the charge IC peaks. However, it is unclear whether other checkerboard patterns can solve the problem. In this paper, we have studied more complicated checkerboard patterns ("modulated checkerboards") by using spin wave theory and analyzed noncollinear checkerboards as well. We find that the high energy response of the modulated checkerboards is inconsistent with neutron scattering results, since they fail to exhibit a resonance peak at (pi,pi), which has recently been shown to be a universal feature of cuprate superconductors. We further argue that the newly proposed noncollinear checkerboard also lacks a resonance peak. We thus conclude that to date no checkerboard pattern has been proposed which satisfies both the low energy constraints and the high energy constraints imposed by the current body of experimental data in cuprate superconductors.Comment: 5 pages, 5 figures, Fig.2 update

Generic susceptibilities of the half-filled Hubbard model in infinite dimensions

Around a metal-to-insulator transition driven by repulsive interaction (Mott transition) the single particle excitations and the collective excitations are equally important. Here we present results for the generic susceptibilities at zero temperature in the half-filled Hubbard model in infinite dimensions. Profiting from the high resolution of dynamic density-matrix renormalization at all energies, results for the charge, spin and Cooper-pair susceptibilities in the metallic and the insulating phase are computed. In the insulating phase, an almost saturated local magnetic moment appears. In the metallic phase a pronounced low-energy peak is found in the spin response.Comment: 12 pages, 12 figures; slight changes and one additional figure due to referees' suggestion

Spin Waves in Quantum Antiferromagnets

Using a self-consistent mean-field theory for the $S=1/2$ Heisenberg antiferromagnet Kr\"uger and Schuck recently derived an analytic expression for the dispersion. It is exact in one dimension ($d=1$) and agrees well with numerical results in $d=2$. With an expansion in powers of the inverse coordination number $1/Z$ ($Z=2d$) we investigate if this expression can be {\em exact} for all $d$. The projection method of Mori-Zwanzig is used for the {\em dynamical} spin susceptibility. We find that the expression of Kr\"uger and Schuck deviates in order $1/Z^2$ from our rigorous result. Our method is generalised to arbitrary spin $S$ and to models with easy-axis anisotropy \D. It can be systematically improved to higher orders in $1/Z$. We clarify its relation to the $1/S$ expansion.Comment: 8 pages, uuencoded compressed PS-file, accepted as Euro. Phys. Lette

On the dynamics of coupled S=1/2 antiferromagnetic zig-zag chains

We investigate the elementary excitations of quasi one-dimensional S=1/2 systems built up from zig-zag chains with general isotropic exchange constants, using exact (Lanczos) diagonalization for 24 spins and series expansions starting from the decoupled dimer limit. For the ideal one-dimensional zig-zag chain we discuss the systematic variation of the basic (magnon) triplet excitation with general exchange parameters and in particular the presence of practically flat dispersions in certain regions of phase space. We extend the dimer expansion in order to include the effects of 3D interactions on the spectra of weakly interacting zig-zag chains. In an application to KCuCl_3 we show that this approach allows to determine the exchange interactions between individual pairs of spins from the spectra as determined in recent neutron scattering experiments.Comment: 8 pages, 9 figures; some changes, figure added; final versio

Three dimensional generalization of the J1J_1-J2J_2 Heisenberg model on a square lattice and role of the interlayer coupling JcJ_c

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg $J_1$-$J_2$ model has been actively discussed recently. However, recent neutron scattering data has shown that the pnictides have a relatively large spin wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the $J_1$-$J_2$-$J_c$ model that is the three dimensional generalization of the $J_1$-$J_2$ Heisenberg model for $S = 1/2$ and S = 1. Using self-consistent spin wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling $J_c$ suppresses the quantum fluctuations and strengthens the long range ordering. In the $J_1$-$J_2$-$J_c$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable upon increasing $J_1$. Either the magnetization or one of the spin wave velocities vanishes. For $S = 1/2$ renormalization due to quantum fluctuations is significantly stronger than for S=1, in particular close to the quantum phase transition. Our findings for the $J_1$-$J_2$-$J_c$ model are of general theoretical interest, however, the results show that it is unlikely that the model is relevant to undoped pnictides.Comment: 11 pages, 10 figures. Updated version, several references adde

Conductivity in a symmetry broken phase: Spinless fermions with 1/d1/d corrections

The dynamic conductivity $\sigma(\omega)$ of strongly correlated electrons in a symmetry broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry broken phase is the charge density wave (CDW) with wave vector $Q=(\pi,\pi,\pi)^\dagger$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e. an expansion in the inverse dimension $1/d$ is used. The finite dimensionality is accounted for by the inclusion of linear terms in $1/d$ and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit $T \to 0$ due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity $\sigma(\omega)$ the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order $1/d$ lead to an excitonic resonance lying within the gap.Comment: 23 pages, 19 figures included with psfig, Revtex; Physical Review B15, in press (October/November 1996) depending on the printer/screen driver, it might be necessary to comment out figures 3,4,5,10,11,12,19 and have them printed separatel