Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz(Oxford Graduate Texts)

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, including condensed 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 integrable forms 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. This makes 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 valuable insight into the physics of strongly correlated quantum matter.

Table of Contents:
1: Introduction Part 1 Methods and Models in the Theory of Quantum Matter 2: Quantum Many-Particle Systems and Second Quantization 3: Angular Momentum 4: Equilibrium Statistical Mechanics 5: Phase Transitions, Critical Phenomena, and Finite-Size Scaling 6: Statistical Mechanics and Quantum Field Theory 7: Conformal Symmetry in Statistical Mechanics 8: Models of Strongly Interacting Quantum Matter Part 2 Algebraic Bethe Ansatz 9: Ice Model 10: General Square Lattice Vertex Models 11: Six-Vertex Model 12: Quantum Tavis-Cummings Model Part 3 Coordinate Bethe Ansatz 13: The Anisotropic Heisenberg Quantum Spin Chain 14: Bethe Ansatz for the Anisotropic Heisenberg Quantum Spin Chain 15: Bose Gas in One Dimension: Lieb-Liniger Model Part 4 Electronic Systems: Nested Bethe Ansatz 16: Electronic Systems Part 5 Thermodynamic Bethe Ansatz 17: Thermodynamics of the Repulsive Lieb-Liniger Model 18: Thermodynamics of the Isotropic Heisenberg Quantum Spin Chain Part 6 Bethe Ansatz for Finite Systems 19: Mathematical Tools 20: Finite Heisenberg Quantum Spin Chain References Index

About the Author :
Hans-Peter Eckles is Adjunct Professor at Ulm University. His research is focused on exactly solvable and integrable models of strongly interacting quantum systems, especially quantum optical models in collaboration with University of Gothenburg, Sweden. He organises and teaches at summer schools in Ireland and Turkey, and is involved with the development and teaching of courses in philosophy of science and research ethics at Ulm University and invited courses on research ethics (e.g. in Aachen, Berlin, Dresden, Freiburg, Göttingen, and Konstanz). Previously, he has taught and conducted research in theoretical physics at Princeton University, University of Arizona, USA, Australian National University and University of New South Wales, Sydney, University, Universities of Tours and Nancy, France, University of Gothenburg, Sweden, University of Jyväskylä, Finland, and University of Hannover and Free University Berlin, Germany.