Free fermions in classical and quantum integrable models

Abstract

This thesis studies the role of free fermions in certain classical and quantum integrable models. The classical models studied are the KP and BKP hierarchies of partial differential equations. We review the presence of free fermions in the theory of these hierarchies, a topic which was established in the work of the Kyoto school. The quantum models studied are descendents and relatives of the XYZ model, or its lattice equivalent, the eight-vertex model. We give a number of new results in the context of these models, revealing the presence of fermions in typical quantities such as Bethe eigenvectors, partition functions and scalar products.

2010 PhD thesis, Department of Mathematics and Statistics, University of Melbourne. 293 pages

References in corpus (11)

• On correlation functions of integrable models associated to the six-vertex R-matrix
• An Izergin-Korepin procedure for calculating scalar products in six-vertex models
• Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold
• Domain wall partition functions and KP
• XXZ scalar products and KP
• BKP plane partitions
• Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry
• On free fermions and plane partitions
• Two elliptic height models with factorized domain wall partition functions
• KP and Toda tau functions in Bethe ansatz
• Phase model expectation values and the 2-Toda hierarchy

Cited by in corpus (6)

• The periodic Schur process and free fermions at finite temperature
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Quantum integrable combinatorics of Schur polynomials
• $Q$-Boson model and relations with integrable hierarchies
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula
• PySymmPol: Symmetric Polynomials in Python