Description of quasiparticle decay by continuous unitary transformations
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Date
2012-07-16
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Abstract
In sufficiently dimerized quantum antiferromagnets the elementary excitations are
given by gapped spin S = 1 triplon quasiparticles. Although these triplons are protected
by a gap at low energies they may decay spontaneously at higher energies where the
one-triplon dispersion merges with the two-triplon continuum.
First, we illustrate and characterize such a spontaneous decay in low-dimensional
quantum antiferromagnets on the basis of a simple one-dimensional bosonic model.
The decay implies the breakdown of the quasiparticle picture. No quantitative description
by a Lorentzian resonance is possible. In particular, three qualitatively different
scenarios are identified depending on the one-triplon dispersion and the two-triplon
interaction.
To describe unstable quasiparticles in more complex models we introduced an
adapted generator for continuous unitary transformations. Its general properties are
derived and discussed.
Next, we investigate asymmetric antiferromagnetic and asymmetric ferroantiferromagnetic
spin S = ½ Heisenberg ladders, which allow for spontaneous
triplon decay, to illustrate this approach. Results for the low-energy spectra and
the dynamical structure factors for these systems are presented. We show that
quasiparticle decay is more pronounced in the case of ferro-antiferromagnetic ladders
than in solely antiferromagnetic ladders.
Finally, we use continuous unitary transformations and high temperature series expansions
to determine a quantitative model for the compound IPA-CuCl3 based on data
of inelastic neutron scattering and measurements of the magnetic susceptibility. Our
calculations reveal IPA-CuCl3 as system of coupled asymmetric spin S = ½ Heisenberg
ladders with the four magnetic couplings J 1 ˜ -2.3 meV, J2 ˜ 1.2 meV, J3 ˜ 2.9 meV and
J4 ˜ -0.3 meV.
Based on this microscopic model for IPA-CuCl3 the adapted continuous unitary
transformation is used to describe the quasiparticle decay in IPA-CuCl3. The results
agree very well with the experimental data. In addition the magnetic field dependence
of the lowest modes in the condensed phase as well as the temperature dependence of
the gap without magnetic field corroborate our microscopic model.
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Keywords
Spinsysteme, Tiefe Temperaturen