An important method of modern theoretical and mathematical physics — the Bethe’s Ansatz (BA) — is introduced to readers. This book presents different forms of the BA for periodic and open quantum chains. Other forms dealt with are the co-ordinate BA, thermodynamic BA, nested BA, algebraic BA, and thermal BA. The book also contains a compact description of other theoretical methods such as scaling, conformal field theory, Abelian and non-Abelian bosonizations.

The book is suitable for use as a textbook by graduate students in non-perturbative methods of low-dimensional quantum many-body theory. It will also be a useful source of reference for qualified physicists, as well as non-experts in low-dimensional physics, as it explores material necessary for further studies in the fields of exactly solvable quantum models and low-dimensional correlated electron systems.

Contents:

• Quantum Spin-˝ Chain with the Nearest-Neighbour Couplings
• Co-Ordinate Bethe Ansatz for a Heisenberg–Ising Ring
• Correlated Electron Chains: Co-Ordinate Bethe Ansatz
• Algebraic Bethe Ansatz
• Correlated Quantum Chains with Open Boundary Conditions
• Correlated Quantum Chains with Isolated Impurities
• Correlated Quantum Chains with a Finite Concentration of Impurities
• Finite Size Corrections in Quantum Correlated Chains
• Beyond the Integrability: Approximate Methods