Multi-particle excitations and spectral densities in quantum spin-systems

The excitation spectrum of the 2-leg S=1/2 Heisenberg ladder is examined perturbatively. Using an optimally chosen continuous unitary transformation we expand the Hamiltonian and the Raman operator about the limit of isolated rungs leading to high order series expansions allowing to calculate spectral densities quantitatively. The 2-particle sector is examined for total momentum k=0. We show that triplet-triplet interaction gives rise to a band splitting.Comment: 2 pages, 1 figure; submitted to the proceedings of the SCES2001 conference (Physica B

Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain

The flow equation method (Wegner 1994) is used as continuous unitary transformation to construct perturbatively effective Hamiltonians. The method is illustrated in detail for dimerized and frustrated antiferromagnetic S=1/2 chains. The effective Hamiltonians conserve the number of elementary excitations which are S=1 magnons for the dimerized chains. The sectors of different number of excitations are clearly separated. Easy-to-use results for the gap, the dispersion and the ground state energies of the chains are provided.Comment: 18 pages, 15 figures included, to appear in Eur. Phys. J. B; Electronic data will be made available on appearance of articl

Perturbative Continuous Unitary Transformations: Spectral Properties of Low Dimensional Spin Systems

In this thesis we describe a novel perturbative approach to low-dimensional quantum many-particle systems, which is based on continuous unitary transformations. We consider systems, which are defined on a lattice and allow a perturbative decomposition. The unperturbed part must have an equidistant spectrum -- the difference between two successive levels is called a quasi-particle. In this case the perturbative transformation leads to an effective Hamiltonian, which conserves the number of particles. The same transformation is used to also derive the effective counterparts of other, experimentally relevant observables. The effective operators are obtained as series expansions in the (small) perturbation parameter. In each order we find a set of products of ladder-operators, which act on states uniquely defined by the number of quasi-particles and their position in the lattice. Thus all calculations can be done in real space. The mathematical structure of the effective operators is extensively analysed. We additionally give all details necessary to implement the method on a computer, which allows the calculation of the effective quantities up to high orders. The method facilitates quantitative calculations of multi-particle excitations and spectral densities of experimentally relevant observables. We include a comprehensive application of the method to the two-dimensional Shastry-Sutherland model, a strongly frustrated quantum spin system. The model has experience an experimental realization by SrCu2(BO3)2. The limit of strong dimerization serves as starting point. Here the ground state is given by singlets on all dimers -- a single triplet constitutes an elementary excitation, i.e. quasi-particle. We quantitatively calculate the one- and two-triplet energies as well as the spectral densities of the Raman and neutron scattering operators. The findings for the spectral densities in particular represent new results. Comparing them to experimental data leads to interesting insights into the spectral properties of low-dimensional quantum spin systems

High Order Perturbation Theory for Spectral Densities of Multi-Particle Excitations: S=1/2 Two-Leg Heisenberg Ladder

We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous unitary transformation introduced previously. It is conceived to work particularly well in models allowing a clear identification of the elementary excitations above the ground state. These are then viewed as quasi-particles above the vacuum. The article focuses on the technical aspects and includes a discussion of series extrapolation schemes. The strength of the method is demonstrated for S=1/2 two-leg Heisenberg ladders, for which results are presented.Comment: 21 pages, 14 figures included; to appear in Eur. Phys. J. B All technical details for the computation of spectral densities by perturbative CUTs Minor misprints removed, references update

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

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

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

Spectral properties of the dimerized and frustrated S=1/2S=1/2 chain

Spectral densities are calculated for the dimerized and frustrated S=1/2 chain using the method of continuous unitary transformations (CUTs). The transformation to an effective triplon model is realized in a perturbative fashion up to high orders about the limit of isolated dimers. An efficient description in terms of triplons (elementary triplets) is possible: a detailed analysis of the spectral densities is provided for strong and intermediate dimerization including the influence of frustration. Precise predictions are made for inelastic neutron scattering experiments probing the S=1 sector and for optical experiments (Raman scattering, infrared absorption) probing the S=0 sector. Bound states and resonances influence the important continua strongly. The comparison with the field theoretic results reveals that the sine-Gordon model describes the low-energy features for strong to intermediate dimerization only at critical frustration.Comment: 21 page

Triplet Dispersion in CuGeO_3: Perturbative Analysis

We reconsider the 2d model for CuGeO_3 introduced previously (Phys. Rev. Lett. 79, 163 (1997)). Using a computer aided perturbation method based on flow equations we expand the 1-triplet dispersion up to 10th order. The expansion is provided as a polynom in the model parameters. The latter are fixed by fitting the theoretical result to experimental data obtained by INS. For a dimerization delta = 0.08(1) we find an excellent agreement with experiment. This value is at least 2 to 3 times higher than values deduced previously from 1d chain approaches. For the intrachain frustration alpha_0 we find a smaller value of 0.25(3). The existence of interchain frustration conjectured previously is confirmed by the analysis of temperature dependent susceptibility.Comment: 8 pages, 10 figures, submitted to Phys. Rev.