Introduction to the Bethe ansatz II

TL;DR

This paper uses the Bethe ansatz to analyze ground-state properties and excitations of the one-dimensional s=1/2 Heisenberg antiferromagnet, providing detailed calculations and numerical methods suitable for graduate students.

Contribution

It introduces detailed procedures for solving Bethe ansatz equations and analyzing excitations in the Heisenberg model, serving as a tutorial for beginners.

Findings

Calculated energies of 2-spinon excitations for finite and infinite chains

Developed numerical methods for solving Bethe ansatz equations

Analyzed ground-state properties under various magnetic fields

Abstract

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.