Description
Oxford Models of Quantum Matter A First Course on Integrability and the Bethe Ansatz 2019 Edition by Hans-Peter Eckle
An important task of theoretical quantum physics is the building of idealized mathematical models to describe the properties of quantum matter. This book provides an introduction to the arguably most important method for obtaining exact results for strongly interacting models of quantum matter - the Bethe ansatz. It introduces and discusses the physical concepts and mathematical tools used to construct realistic models for a variety of different fields, includingcondensed matter physics and quantum optics. The various forms of the Bethe ansatz - algebraic, coordinate, multicomponent, and thermodynamic Bethe ansatz, and Bethe ansatz for finite systems - are then explained in depth and employed to find exact solutions for the physical properties of the integrableforms of strongly interacting quantum systems.The Bethe ansatz is one of the very few methodologies which can calculate physical properties non-perturbatively. Arguably, it is the only such method we have which is exact. This means, once the model has been set up, no further approximations or assumptions are necessary, and the relevant physical properties of the model can be computed exactly. Furthermore, an infinite set of conserved quantities can be obtained. The quantum mechanical model under consideration is fully integrable. Thismakes the search for quantum models which are amenable to an exact solution by the Bethe ansatz, and which are quantum integrable, so important and rewarding. The exact solution will provide benchmarks for other models, which do not admit an exact solution. Bethe ansatz techniques provide valuableinsight into the physics of strongly correlated quantum matter. Table of contents : - 1: IntroductionPart 1 Methods and Models in the Theory of Quantum Matter2: Quantum Many-Particle Systems and Second Quantization3: Angular Momentum4: Equilibrium Statistical Mechanics5: Phase Transitions, Critical Phenomena, and Finite-Size Scaling6: Statistical Mechanics and Quantum Field Theory7: Conformal Symmetry in Statistical Mechanics8: Models of Strongly Interacting Quantum MatterPart 2 Algebraic Bethe Ansatz9: Ice Model10: General Square Lattice Vertex Models11: Six-Vertex Model12: Quantum Tavis-Cummings ModelPart 3 Coordinate Bethe Ansatz13: The Anisotropic Heisenberg Quantum Spin Chain14: Bethe Ansatz for the Anisotropic Heisenberg Quantum Spin Chain15: Bose Gas in One Dimension: Lieb-Liniger ModelPart 4 Electronic Systems: Nested Bethe Ansatz16: Electronic SystemsPart 5 Thermodynamic Bethe Ansatz17: Thermodynamics of the Repulsive Lieb-Liniger Model18: Thermodynamics of the Isotropic Heisenberg Quantum Spin ChainPart 6 Bethe Ansatz for Finite Systems19: Mathematical Tools20: Finite Heisenberg Quantum Spin ChainReferences Index