The Bethe WavefunctionMichel 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. |
Contents
The chain of spin12 atoms | 1 |
2 | 27 |
Limiting cases | 44 |
δInteracting bosons | 54 |
Bethe wavefunctions associated with a reflection group | 79 |
Continuum limit of the spin chain | 94 |
The sixvertex model | 112 |
The eightvertex model | 142 |
General solution for | 223 |
Appendix | 239 |
1 | 250 |
General solution for | 253 |
27 | 259 |
Various corollaries and extensions | 268 |
On the Toda chain | 301 |
| 314 | |
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Common terms and phrases
according algebra amplitude analogous antisymmetric arbitrary associated Baxter Bethe’s bosons boundary calculation Chapter coefficients commuting configuration consider corresponding cosh coupled equations cyclic deduce defined definition density determined diagonal domain eigenstate eigenvalue eigenvector eight-vertex model elliptic equivalent exists expression fermion ferroelectric field find finite first formula Fourier free energy function Gaudin given gives Hamiltonian hypothesis identical particles identity inhomogeneous integral equation interaction invariance Ising model magnetization matrix elements method momenta notation obtain operators parameters particles periodicity conditions permutation problem Proposition quantities quantum numbers representation right-hand side sector singularity sinh six-vertex model solution spectrum spin chain square lattice string Subsection sufficient symmetry ternary relations thermodynamic limit total spin transfer matrix transformation vanishes variables verify vertex vertex configuration vertex model vertices wavefunction write written Yang’s Young tableau zero