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Integrable lattice models for strongly correlated electrons

Eoin Quinn

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

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.

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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.
We consider two lattice models for strongly correlated electrons which are exactly solvable in one dimension. Along with the Hubbard model and the spin chain, these are the only parity-invariant models that can be obtained from Shastry's R -matrix. One exhibits itinerant ferromagnetic behaviour, while for the other the electrons form bound pairs and at half-filling the model becomes insulating. We derive the thermodynamic Bethe ansatz equations for the models, analyse them at various limits, and in particular obtain zero temperature phase diagrams. Furthermore, we consider extensions of the models, which reduce to the Essler–Korepin–Schoutens model in certain limits.
Integrability of strongly correlated electron systems on open chains XIANG-YU GEIn recent years, there has been a strong increase of interest in models of strongly correlated electron systems in condensed matter physics, in particular in integrable onedimensional models.Examples of such models are the one-dimensional Hubbard model, the supersymmetric t-J model, the Hubbard-like model (Bariev's chain), the so-called extended Hubbard model (EKS model), the supersymmetric U model and the eight-state supersymmetric U model.The study of integrable open-boundary conditions for strongly correlated electron models is very important for physical applications, especially for gaining insights into the behaviour of more realistic systems.The important ingredient in Sklyanin's boundary quantum inverse scattering method (QISM), which has played a key role in recent advances in the study of lattice models with open-boundaries, is a new algebraic structure, the reflection equation algebra.In this thesis, a general graded reflection equation algebra is proposed and the corresponding graded (supersymmetry) boundary QISM is formulated.The formalism is applicable to all boundary lattice systems where an invertible i?-matrix exists.As applications, some important integrable boundary conditions for various strongly correlated electron models with quantum superalgebra symmetries are constructed, including:1. Presentation of integrable open-boundary conditions for the one-dimensional qdeformed supersymmetric Essler-Korepin-Schoutens (EKS) extended Hubbard model.Determination of three different diagonal boundary if-matrices and of nine classes of integrable open-boundary conditions.Construction of the exactly solvable Hamiltonian with open-boundary terms for quantum superalgebra U q (gl(2\2)) symmetry; 2. Establishment of the quantum integrability of open-boundary conditions for the one-dimensional ^-deformed supersymmetric U model with quantum superalgebra U q (gl(2\l)} symmetry.Determination of diagonal boundary if-matrices and of integrable open-boundary conditions.Solution of the boundary system by means of the coordinate space Bethe ansatz technique, and derivation of the Bethe ansatz equations;