The Bethe Wavefunction

Michel Gaudin, Jean-Sébastien Caux

• Publisher: Cambridge University Press
• Year: 2014
• Print ISBN: 9781107045859
• eBook ISBN: 9781107777200
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first time, this translation brings his classic work to a new generation of graduate students and researchers in physics. It presents a mixture of mathematics interspersed with powerful physical intuition, retaining the author's unmistakably honest tone. The book begins with the Heisenberg spin chain, starting from the coordinate Bethe Ansatz and culminating in a discussion of its thermodynamic properties. Delta-interacting bosons (the Lieb-Liniger model) are then explored, and extended to exactly solvable models associated to a reflection group. After discussing the continuum limit of spin chains, the book covers six- and eight-vertex models in extensive detail, from their lattice definition to their thermodynamics. Later chapters examine advanced topics such as multi-component delta-interacting systems, Gaudin magnets and the Toda chain.

Table of contents

• Cover
• Half-title Page
• Epigraph
• Title Page
• Copyright Page
• Contents
• Foreword
• Translator's note
• Introduction
• 1 The chain of spin-1/2 atoms
• 2 Thermodynamic limit of the Heisenberg–Ising chain
• 3 Thermodynamics of the spin-1/2 chain: Limiting cases
• 4 δ-Interacting bosons
• 5 Bethe wavefunctions associated with a reflection group
• 6 Continuum limit of the spin chain
• 7 The six-vertex model
• 8 The eight-vertex model
• 9 The eight-vertex model: Eigenvectors and thermodynamics
• 10 Identical particles with δ-interactions
• 11 Identical particles with δ-interactions: General solution for two internal states
• 12 Identical particles with δ-interactions: General solution for n components and limiting cases
• 13 Various corollaries and extensions
• 14 On the Toda chain
• References
• Index