Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1998-10-11
Nonlinear Sciences
Exactly Solvable and Integrable Systems
PhD dissertation. In French. the articles are not included (they're already on the archive)
Scientific paper
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex models) and relativistic field theories with 1 space dimension and 1 time dimension. The connection with quantum groups is expounded. Several applications are then presented. Finite size corrections are calculated via two methods: The Non-Linear Integral Equations, which are applied to the study of the states of the affine Toda model with imaginary coupling, and their interpolation between the high energy (ultra-violet) and low energy (infra-red) regions; and the Thermodynamic Bethe Ansatz Equations, along with the associated Fusion Equations, which are used to determine the thermodynamic properties of the generalized multi-channel Kondo model. The latter is then studied in more detail, still using the Bethe Ansatz and quantum groups, so as to characterize the spectrum of the low energy excitations.
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