Models of Quantum Matter

Abstract

AbstractThis book focuses on the theory of quantum matter, strongly interacting systems of quantum many–particle physics, particularly on their study using exactly solvable and quantum integrable models with Bethe ansatz methods. Part 1 explores the fundamental methods of statistical physics and quantum many–particle physics required for an understanding of quantum matter. It also presents a selection of the most important model systems to describe quantum matter ranging from the Hubbard model of condensed matter physics to the Rabi model of quantum optics. The remaining five parts of the book examines appropriate special cases of these models with respect to their exact solutions using Bethe ansatz methods for the ground state, finite–size, and finite temperature properties. They also demonstrate the quantum integrability of an exemplary model, the Heisenberg quantum spin chain, within the framework of the quantum inverse scattering method and through the algebraic Bethe ansatz. Further models, whose Bethe ansatz solutions are derived and examined, include the Bose and Fermi gases in one dimension, the one–dimensional Hubbard model, the Kondo model, and the quantum Tavis–Cummings model, the latter a model descendent from the Rabi model.