Models of Quantum matter : a first course on integrability and the Bethe Ansatz First Edition Eckle

Models of Quantum matter : a first course on integrability and the Bethe Ansatz – Ebook Instant Download/Delivery ISBN(s): 9780199678839,0199678839

Product details:

• ISBN-10 ‏ : ‎ 0199678839
• ISBN-13 ‏ : ‎ 978-0199678839
• Author(s): Eckle, Hans-Peter

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 contents:

Chapter 1: Introduction
Part 1: Methods and Models in the Theory of Quantum Matter
Chapter 2: Quantum Many-Particle Systems and Second Quantization

Chapter 3: Angular Momentum

Chapter 4: Equilibrium Statistical Mechanics

Chapter 5: Phase Transitions, Critical Phenomena, and Finite-Size Scaling

Chapter 6: Statistical Mechanics and Quantum Field Theory

Chapter: 7: Conformal Symmetry in Statistical Mechanics

Chapter 8: Models of Strongly Interacting Quantum Matter

Part 2: Algebraic Bethe Ansatz
Chapter 9: Ice Model

Chapter 10: General Square Lattice Vertex Models

Chapter 11: Six-Vertex Model

References
Index

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