14 research outputs found
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
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
Unified Quantum Mechanical Picture for Confined Spinons in Dimerized and Frustrated Spin S=1/2 Chains
A quantum mechanical picture is presented to describe the behavior of
confined spinons in a variety of S=1/2 chains. The confinement is due to
dimerization and frustration and it manifests itselfas a nonlinear potential
V(x)~ |x|^b, centered at chain ends (b <= 1) or produced by modulation kinks (b
> 1). The calculation extends to weak or zero frustration some previous ideas
valid for spinons in strongly frustrated spin chains. The local magnetization
patterns of the confined spinons are calculated. A (minimum) enhancement of the
local moments of about 11/3 over a single S=1/2 is found. Estimates for
excitation energies and binding lengths are obtained.Comment: 11.5 pages, Revtex, 10 figures included, accepted by Euro. Phys. J. B
final version including some changes, several references adde