Introduction to the Bethe Ansatz

This ongoing series of papers is designed as a tutorial for beginning graduate students.
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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