Each article includes problems for further study.

M. Karbach and G. Müller

**Introduction to the Bethe ansatz I.**

Computers in Physics 11 (1997), 36-43.
[cond-mat/9809162]

http://digitalcommons.uri.edu/phys_facpubs/45/

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.

M. Karbach, K. Hu, and G. Müller

**Introduction to the Bethe ansatz II.**

Computers in Physics 12 (1998), 565-573.
[cond-mat/
9809163]

http://digitalcommons.uri.edu/phys_facpubs/46/

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.

M. Karbach, K. Hu, and G. Müller

Introduction to the Bethe ansatz III.

[cond-mat/ 0008018]

http://digitalcommons.uri.edu/phys_facpubs/47/

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.

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