arXiv subjects
Publications and source records attributed to Gerhard Muller.
The Bethe ansatz for the one-dimensional s=1/2 Heisenberg ferromagnet is introduced at an elementary level. The presentation follows Bethe's original work very closely. A detailed description and a complete classification of all two-magnon scattering states and two-magnon bound states are given for finite and infinite chains. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.
Building on the fundamentals introduced in part I, we employ the Bethe ansatz to study some ground-state properties (energy, magnetization, susceptibility) of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero magnetic field. The 2-spinon triplet and singlet excitations from the zero-field ground state are discussed in detail, and their energies are calculated for finite and infinite chains. Procedures for the numerical calculation of real and complex solutions of the Bethe ansatz equations are discussed and applied. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.
We consider a two-spin model, represented classically by a nonlinear autonomous Hamiltonian system with two degrees of freedom and a nontrivial integrability condition, and quantum mechanically by a real symmetric Hamiltonian matrix with blocks of dimensionalities K=l(l+1)/2, l=1,2,... In the six-dimensional (6D) parameter space of this model, classical integrability is satisfied on a 5D hypersurface, and level crossings occur on 4D manifolds that are completely embedded in the integrability hypersurface except for some lower-D sub-manifolds. Under mild assumptions, the classical integrability condition can be reconstructed from a purely quantum mechanical study of level degeneracies in finite-dimensional invariant blocks of the Hamiltonian matrix. Our conclusions are based on rigorous results for K=3 and on numerical results for K=6,10.