Michael Karbach

Two-spinon dynamic structure factor of the one-dimensional s=1/2 Heisenberg antiferromagnet

The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q,v) of the one-dimensional s51/2 Heisenberg antiferromagnet at T5 0i s evaluated for direct comparison with finite-chain transition rates (N<28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q,v). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and q dependent susceptibility are determined via sum rules. The impact of the non-twospinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q,v) is studied on the basis of finite-size data. @S0163-1829~97!00517-1#

Introduction to the Bethe Ansatz II

Having introduced the magnon in part I and the spinon in part II as the relevant quasi-particles for the interpretation of the spectrum of low-lying excitations in the one-dimensional (1D) s=1/2 Heisenberg ferromagnet and antiferromagnet, respectively, we now study the low-lying excitations of the Heisenberg antiferromagnet in a magnetic field and interpret these collective states as composites of quasi-particles from a different species. We employ the Bethe ansatz to calculate matrix elements and show how the results of such a calculation can be used to predict lineshapes for neutron scattering experiments on quasi-1D antiferromagnetic compounds. The paper is designed as a tutorial for beginning graduate students. It includes 11 problems for further study.

Exact Two-spinon Dynamic Structure Factor of the One-dimensional s=1/2 Heisenberg-Ising Antiferromagnet

The exact 2-spinon part of the dynamic spin structure factor

Transition rates via Bethe ansatz for the spin-½ Heisenberg chain

S_{xx}(Q,\omega)

Line-shape predictions via Bethe ansatz for the one-dimensional spin- 1 2 Heisenberg antiferromagnet in a magnetic field

for the one-dimensional

Transition Rates via Bethe Ansatz for the Spin-1/2 Planar XXZ Antiferromagnet

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Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field

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Thermodynamics of ideal quantum gas with fractional statistics in D dimensions.

XXZ

Spinon Excitations in the XX Chain: Spectra, Transition Rates, Observability

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Spectrum and transition rates of the XX chain analyzed via Bethe ansatz

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