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

Varied Perturbation Theory for the Dispersion Dip in the Two-Dimensional Heisenberg Quantum Antiferromagnet

We study the roton-like dip in the magnon dispersion at the boundary of the Brillouin zone in the isotropic S=1/2 Heisenberg quantum antiferromagnet. This high-energy feature is sometimes seen as indication of a fractionalization of the magnons to spinons. In this article, we provide evidence that the description of the dip in terms of magnons can be improved significantly by applying more advanced evaluation schemes. In particular, we illustrate the usefulness of the application of the principle of minimal sensitivity in varied perturbation theory. Thereby, we provide an example for the application of this approach to an extended condensed matter problem governed by correlations which can trigger analogous investigations for many other systems.Comment: Published versio

Wave Dark Matter and the Tully-Fisher Relation

We investigate a theory of dark matter called wave dark matter, also known as scalar field dark matter (SFDM) and boson star dark matter or Bose-Einstein condensate (BEC) dark matter, in spherical symmetry and its relation to the Tully-Fisher relation. We show that fixing the oscillation frequency of wave dark matter near the edge of dark galactic halos implies a Tully-Fisher-like relation for those halos. We then describe how this boundary condition, which is roughly equivalent to fixing the half-length of the exponentially decaying tail of each galactic halo mass profile, may yield testable predictions for this theory of dark matter.Comment: 19 pages, 4 figure

Effects of ring exchange interaction on the Neel phase of two-dimensional, spatially anisotropic, frustrated Heisenberg quantum antiferromagnet

Higher order quantum effects on the magnetic phase diagram induced by four-spin ring exchange on plaquettes are investigated for a two-dimensional quantum antiferromagnet with S=1/2. Spatial anisotropy and frustration are allowed for. Using a perturbative spin-wave expansion up to second order in 1/S we obtain the spin-wave energy dispersion, sublattice magnetization, and the magnetic phase diagram. We find that for substantial four-spin ring exchange the quantum fluctuations are stronger than in the standard Heisenberg model. A moderate amount of four-spin ring exchange couplings stabilizes the ordered antiferromagnetic Neel state while a large amount renders it unstable. Comparison with inelastic neutron scattering data points toward a moderate ring exchange coupling of 27% to 29% of the nearest-neighbor exchange coupling.Comment: 10 figures, minor editorial changes in the published versio

High Temperature Expansion for Frustrated and Unfrustrated S=1/2 Spin Chains

A computer aided high temperature expansion of the magnetic susceptibility and the magnetic specific heat is presented and demonstrated for frustrated and unfrustrated spin chains. The results are analytic in nature since the calculations are performed in the integer domain. They are provided in the form of polynomials allowing quick and easy fits. Various representations of the results are discussed. Combining high temperature expansion coefficients and dispersion data yields very good agreement already in low order of the expansion which makes this approach very promising for the application to other problems, for instance in higher dimensions.Comment: 13 pages, 8 figures, to appear in Eur. Phys. J. B, minor corrections, correction of a[5] in table A.1.a, discussion of the region of validity added, coefficients available electronically: http://www.thp.uni-koeln.de/~g