by Zachary N C Ha (Institute for Advanced Study, USA)

The main theme of the book is the intimate connection between the two families of exactly solvable models: the inverse-square exchange (ISE) and the nearest-neighbor exchange (NNE) models. The latter are better known as the Bethe-Ansatz solvable models and include the Heisenberg spin chain, t–J models and Hubbard models. The former, the Calogero–Sutherland family of models, are simple to solve and contain essentially the same physics as the NNE family. The author introduces and discusses current topics, such as the Luttinger liquid concept, fractional statistics, and spin–charge separation, in the context of the explicit models.

• Introduction
• Heisenberg Spin Chain
• The 1D Hubbard Model
• Models with Inverse-Square Exchange
• Strings in Long-Range Interaction Model
• Elementary Excitations of t-J Model
• Fractional Statistics in One-Dimension: View from an Exactly Solvable Model
• Concluding Remarks