The One-Dimensional Hubbard Model

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This book presents a self-contained account of the exact solution of the Hubbard model in one dimension. The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents. It is impossible to solve the corresponding many-body problems, although insight can be gained from analysis of simplified models. An important example is the Hubbard model, which describes interacting electrons in narrow energy bands and which has been applied to a diverse range of problems.

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Editorial Reviews

From the Publisher
"The joint expertise of the authors on the subject is formidable. The influence of their intimate familiarity with the material is visible throughout the book. The bibliography is extensive and will be a useful tool for those interested in the original publications. Short of asking an expert, there is no better way to access the huge body of work accumulated over decades by a large number of authors. Every physics and chemistry library should have a copy of this book, and many individual researchers want to have a copy on their shelves, too."
Bruno Nachtergaele, University of California, Davis, SIAM Review
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Product Details

  • ISBN-13: 9780521802628
  • Publisher: Cambridge University Press
  • Publication date: 2/7/2005
  • Pages: 690
  • Product dimensions: 6.85 (w) x 9.72 (h) x 1.81 (d)

Table of Contents

Preface; 1. Introduction; 2. The Hubbard Hamiltonian and its symmetries; 3. The Bethe ansatz solution; 4. String hypothesis; 5. Thermodynamics in the Yang-Yang approach; 6. Ground state properties in the thermodynamic limit; 7. Excited states at zero temperature; 8. Finite size corrections at zero temperature; 9. Asymptotics of correlation functions; 10. Scaling and continuum limits at half-filling; 11. Universal correlations at low density; 12. The algebraic approach to the Hubbard model; 13. The path integral approach to thermodynamics; 14. The Yangian symmetry of the Hubbard model; 15. S-matrix and Yangian symmetry in the infinite interval limit; 16. Hubbard model in the attractive case; 17. Mathematical appendices; References; Index.

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