Quantum spin chains: dynamics and statistics of quasiparticles
1D s=1/2 XXZ antiferromagnet:
- Coordinate Bethe ansatz,
- string solutions: magnon scattering states and bound states,
- XX and XXX limits,
- XXX spectrum from magnon and spinon perspectives,
- XX spectrum from magnon, spinon, and Jordan-Wigner fermion
perspectives.
Haldane-Shastry model:
- Haldane-Shastry spectrum from magnon and spinon perspectives.
Fractional exclusion statistics:
- counting rules for fermions, spinons, and magnons,
- application to XXX model, XX model, and Haldane-Shastry
model.
Quantum fluctuations at equilibrium:
- excitation spectrum, quasiparticles, selection rules, and
dynamic structure factors,
- observation via inelastic magnetic neutron scattering.
Rigorous methods for dynamic correlations:
- algebraic analysis (quantum group symmetries),
- algebraic Bethe ansatz,
- Jordan-Wigner fermions (XX model),
- Yangian algebra (Haldane-Shastry model).
Two-spinon dynamic structure factors:
- exact results for XX, XXX, XXZ, and Haldane-Shastry models,
- comparison with magnetic neutron scattering data.
Transition rates via algebraic Bethe ansatz:
- XXX model,
- XXZ model,
- XX limit.