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Models of Quantum Matter

A First Course on Integrability and the Bethe Ansatz

Hans-Peter Eckle

July 2019

ISBN: 9780199678839

732 pages
Hardback
246x171mm

In Stock

Oxford Graduate Texts

Price: £69.00

The book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.

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Description

The book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.

  • Accessible introductory text on the Bethe Ansatz, suitable for graduate and advanced undergraduate students
  • Generous discussion of the physical properties of models
  • Models are introduced in a pedagogical fashion, making it a perfect course companion
  • Examples and exercises throughout provide a hands-on experience, cementing readers' newfound knowledge

About the Author(s)

Hans-Peter Eckle, Adjunct Professor, Humboldt Study Centre, Ulm University, Germany

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.

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

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