Dynamics of One-Dimensional Quantum Systems: Inverse-Square Interaction Models

Dynamics of One-Dimensional Quantum Systems: Inverse-Square Interaction Models

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Yoshio Kuramoto
Cambridge University Press
Edition: Reprint, 8/7/2014
EAN 9781107424722, ISBN10: 1107424720

Paperback, 488 pages, 24.4 x 17 x 2.8 cm
Language: English

One-dimensional quantum systems show fascinating properties beyond the scope of the mean-field approximation. However, the complicated mathematics involved is a high barrier to non-specialists. Written for graduate students and researchers new to the field, this book is a self-contained account of how to derive the exotic quasi-particle picture from the exact solution of models with inverse-square interparticle interactions. The book provides readers with an intuitive understanding of exact dynamical properties in terms of exotic quasi-particles which are neither bosons nor fermions. Powerful concepts, such as the Yangian symmetry in the Sutherland model and its lattice versions, are explained. A self-contained account of non-symmetric and symmetric Jack polynomials is also given. Derivations of dynamics are made easier, and are more concise than in the original papers, so readers can learn the physics of one-dimensional quantum systems through the simplest model.

1. Introduction
Part I. Physical Properties
2. Single-component Sutherland model
3. Multi-component Sutherland model
4. Spin chain with 1/r2 interactions
5. SU(K) spin chain
6. Supersymmetric t-J model with 1/r2 interaction
Part II. Mathematics Related to 1/r2 Systems
7. Jack polynomials
8. Yang-Baxter relations and orthogonal eigenbasis
9. SU(K) and supersymmetric Yangians
10. Uglov's theory
List of symbols