Studies in Integrable Quantum Lattice Models and Classical Hierarchies

Abstract

The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns itself mainly with correlations between results in classical hierarchies and quantum lattice models. The second part, consisting of chapters 4-6, deals almost entirely with deriving results concerned with quantum lattice models.

PhD Thesis, 210 pages, 51 figures (metadata added in v2)

References in corpus (6)

• Nonlinear Integral Equations and high temperature expansion for the $U_q(\widehat{sl}(r+1|s+1))$ Perk-Schultz Model
• XXZ scalar products and KP
• Izergin-Korepin determinant reloaded
• Two elliptic height models with factorized domain wall partition functions
• Gaudin functions, and Euler-Poincaré characteristics
• Phase model expectation values and the 2-Toda hierarchy

Cited by in corpus (4)

• KP and Toda tau functions in Bethe ansatz
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Elliptic supersymmetric integrable model and multivariable elliptic functions
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula