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Soviet Journal of Low Temperature Physics

Theory of weakly bound states of quasiparticles

I.V. Baryakhtar

Published Mar 1, 1987• 0 citations
Publisher

Abstract

The dependence of the binding energy of two quasiparticles on the total momentum is determined for quasiparticles with the dispersion law ϵ = ϵ0[1 + γ (ak)n] and interacting via an arbitrarily weak interaction. The asymptotics of the wave function of two quasiparticles in a bound state is determined in the one-, two-, and three-dimensional cases.

DOI
10.1063/10.0031671

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The dependence of the binding energy of two quasiparticles on the total momentum is determined for quasiparticles with the dispersion law ϵ = ϵ0[1 + γ (ak)n] and interacting via an arbitrarily weak interaction. The asymptotics of the wave function of two quasiparticles in a bound state is determined in the one-, two-, and three-dimensional cases.
The spectra and the necessary criteria for the existence of a bound state of a pair of activation or Goldstone quasiparticles, whose energy depends on the momentum according to a power law with index n ≤ 2, are derived. In a space of dimensions d ≥ 2 a bound state forms with an arbitrarily weak attraction independently of the magnitude of the total momentum of the pair 2Q, while in a space of dimension > 2 the bound state forms only it 2Q is less than a critical value 2Qc. For Q > Qc the bound state is destroyed by a kinetic mechanism.
Interactions between elementary excitations in quasi-one-dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wave functions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (nonintegrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasiparticle excitations are bound states of topological solitons. The spin structure factor involving two quasiparticle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.
We study the structure of bound states appearing in systems governed by the Coulomb and short-range interactions. We analyze the binding energies and wave functions of the bound states generated by the Coulomb plus short-range potential. We demonstrate that Coulomb-induced shifts of the binding energy are closely correlated with the spatial distribution of the wave function. Furthermore, we show that the asymptotic behavior of wave functions of weakly bound states is qualitatively altered by Coulomb repulsion, leading to a modification of the near-threshold mass scaling that is otherwise universal for short-range interactions.