Raman Response in Antiferromagnetic Two-Leg S=1/2 Heisenberg Ladders

The Raman response in the antiferromagnetic 2-leg S=1/2 Heisenberg ladder is calculated for various couplings by continuous unitary transformations. For leg couplings above 80% of the rung coupling a characteristic 2-peak structure occurs with a point of zero intensity within the continuum. Experimental data for CaV_2O_5 and La_yCa_(14-y)Cu_24O_41 are analyzed and the coupling constants are determined. Evidence is found that the Heisenberg model is not sufficient to describe cuprate ladders. We argue that a cyclic exchange term is the appropriate extension.Comment: 4 pages with 4 figures include

The Structure of Operators in Effective Particle-Conserving Models

For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians conserving the number of excitations. The same transformation must be used to obtain effective observables. The analysis of the structure shows that effective operators give rise to a simple and intuitive perspective on the initial problem. The systematic calculation of n-particle irreducible quantities becomes possible constituting a significant progress. Details how to implement the approach perturbatively for a large class of systems are presented.Comment: 12 pages, 1 figure, accepted by J. Phys. A: Math. Ge

SrCu_2(BO_3)_2 - a Two Dimensional Spin Liquid

We study an extended Shastry-Sutherland model for SrCu_2(BO_3)_2 and analyze the low lying parts of the energy spectrum by means of a perturbative unitary transformation based on flow equations. The derivation of the 1-magnon dispersion (elementary triplets) is discussed. Additionally, we give a quantitative description (symmetries and energies) of bound states made from two elementary triplets. Our high order results allow to fix the model parameters for SrCu_2(BO_3)_2 precisely: J_1=6.16(10)meV, x:=J_2/J_1=0.603(3), J_\perp=1.3(2)meV. To our knowledge this is the first quantitative treatment of bound states in a true 2d model.Comment: 4 pages, 3 figures, Proceeding paper of the HFM2000 conference in Waterloo, Canada, Jun 200

Symmetries and Triplet Dispersion in a Modified Shastry-Sutherland Model for SrCu_2(BO_3)_2

We investigate the one-triplet dispersion in a modified Shastry-Sutherland Model for SrCu_2(BO_3)_2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy quanta conserving block diagonal Hamiltonian H_{eff}. The dispersion splits into two branches which are nearly degenerated. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k=0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small |k| and compare our results to INS data.Comment: 9 pages, 8 figures accepted by J. Phys.: Condens. Matte

Quasiparticle Dynamics in the Kondo Lattice Model at Half Filling

We study spectral properties of quasiparticles in the Kondo lattice model in one and two dimensions including the coherent quasiparticle dispersions, their spectral weights and the full two-quasiparticle spectrum using a cluster expansion scheme. We investigate the evolution of the quasiparticle band as antiferromagnetic correlations are enhanced towards the RKKY limit of the model. In both the 1D and the 2D model we find that a repulsive interaction between quasiparticles results in a distinct antibound state above the two-quasiparticle continuum. The repulsive interaction is correlated with the emerging antiferromagnetic correlations and can therefore be associated with spin fluctuations. On the square lattice, the antibound state has an extended s-wave symmetry.Comment: 8 pages, 11 figure

Raman Response of Magnetic Excitations in Cuprate Ladders and Planes

An unified picture for the Raman response of magnetic excitations in cuprate spin-ladder compounds is obtained by comparing calculated two-triplon Raman line-shapes with those of the prototypical compounds SrCu2O3 (Sr123), Sr14Cu24O41 (Sr14), and La6Ca8Cu24O41 (La6Ca8). The theoretical model for the two-leg ladder contains Heisenberg exchange couplings J_parallel and J_perp plus an additional four-spin interaction J_cyc. Within this model Sr123 and Sr14 can be described by x:=J_parallel/J_perp=1.5, x_cyc:=J_cyc/J_perp=0.2, J_perp^Sr123=1130 cm^-1 and J_perp^Sr14=1080 cm^-1. The couplings found for La6Ca8 are x=1.2, x_cyc=0.2, and J_perp^La6Ca8=1130 cm^-1. The unexpected sharp two-triplon peak in the ladder materials compared to the undoped two-dimensional cuprates can be traced back to the anisotropy of the magnetic exchange in rung and leg direction. With the results obtained for the isotropic ladder we calculate the Raman line-shape of a two-dimensional square lattice using a toy model consisting of a vertical and a horizontal ladder. A direct comparison of these results with Raman experiments for the two-dimensional cuprates R2CuO4 (R=La,Nd), Sr2CuO2Cl2, and YBa2Cu3O(6+delta) yields a good agreement for the dominating two-triplon peak. We conclude that short range quantum fluctuations are dominating the magnetic Raman response in both, ladders and planes. We discuss possible scenarios responsible for the high-energy spectral weight of the Raman line-shape, i.e. phonons, the triple-resonance and multi-particle contributions.Comment: 10 pages, 6 figure

Optical spectroscopy of (La,Ca)14Cu24O41 spin ladders: comparison of experiment and theory

Transmission and reflectivity of La_x Ca_14-x Cu_24 O_41 two-leg spin-1/2 ladders were measured in the mid-infrared regime between 500 and 12000 1/cm. This allows us to determine the optical conductivity sigma_1 directly and with high sensitivity. Here we show data for x=4 and 5 with the electrical field polarized parallel to the rungs (E||a) and to the legs (E||c). Three characteristic peaks are identified as magnetic excitations by comparison with two different theoretical calculations.Comment: 4 pages, 2 figures, submitted to SCES 200

Dispersion and Symmetry of Bound States in the Shastry-Sutherland Model

Bound states made from two triplet excitations on the Shastry-Sutherland (ShaSu) lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results (up to (J_2/J_1)^{14}) permit to fix the parameters of SrCu_2(BO_3)_2 precisely: J_1=6.16(10)meV, x:=J_2/J_1=0.603(3), J_\perp=1.3(2)meV. At the border of the magnetic Brillouin zone (MBZ) a general double degeneracy is derived. An unexpected instability in the triplet channel at x=0.63 indicates a first order transition towards a triplet condensate, related to classical helical order.Comment: 4 pages, submitted to Phys. Rev. Let

The Equivalence Theorem and Effective Lagrangians

We point out that the equivalence theorem, which relates the amplitude for a process with external longitudinally polarized vector bosons to the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a more general formulation of this theorem also holds for effective interactions. The generalized theorem can be utilized to determine the high-energy behaviour of scattering processes just by power counting and to simplify the calculation of the corresponding amplitudes. We apply this method to the phenomenologically most interesting terms describing effective interactions of the electroweak vector and Higgs bosons in order to examine their effects on vector-boson scattering and on vector-boson-pair production in $f\bar{f}$ annihilation. The use of the equivalence theorem in the literature is examined.Comment: 20 pages LaTeX, BI-TP 94/1