Lattice Construction of Quantum Integrable Systems

Mo‐Lin Ge

Rei Inoue, Kazuhiro Hikami

We construct the quantum integrable dynamical system on a (2+1)-dimensional lattice. We consider the q -commuting operators on 2-D lattice as a discretization of the current algebra, and two evolution operators are explicitly defined in terms of the quantum dilogarithm function.

Kazuhiro Hikami, Rei Inoue

We investigate the integrable structure of the quantum Volterra model, which is a discretization of the Korteweg–de Vries equation. Based on Sklyanin's method we derive the Baxter equation, and then clarify a role of the “fundamental transfer matrix”. We show that the fundamental transfer matrix also generates the integrals of motion for a lattice analogue of the sine–Gordon system.

Shuichi Murakami

Eoin Quinn

This thesis is dedicated to the study of a new family of integrable lattice models for strongly correlated electrons, namely the Hubbard- Shastry models. The techniques of exactly solvable models, and in particular those of integrable systems, are used. The models are constructed through the quantum inverse scattering method and are studied in one dimension through their Bethe ansatz solution.

Michael Fowler