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The One-Dimensional Hubbard Model
Abstract
The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. It is impossible to solve the corresponding many-body problems analytically or numerically, although much insight can be gained from the 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 problems as diverse as high-Tc superconductivity, band magnetism, and the metal-insulator transition. This 2005 book presents a coherent, self-contained account of the exact solution of the Hubbard model in one dimension. The early chapters will be accessible to beginning graduate students with a basic knowledge of quantum mechanics and statistical mechanics. The later chapters address more advanced topics, and are intended as a guide for researchers to some of the more topical results in the field of integrable models.
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Citations
Cited by
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen(De), A., & Sen, U. (2007) · Advances in Physics · doi:10.1080/00018730701223200 · Cited by 2,104
“ns and correlations is particularly important in 1D. The theory of 1D systems is very well developed due to existence of exact methods such as Bethe ansatz and quantum inverse scattering theory (c.f. [45]), powerful approximate approaches, such as bosonisation, or conformal field theory [46], and efficient computational…”
BackgroundMethodQuench dynamics and relaxation in isolated integrable quantum spin chains
Essler, F. H. L., & Fagotti, M. (2016) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2016/06/064002 · Cited by 668
Self-citationFIDELITY APPROACH TO QUANTUM PHASE TRANSITIONS
GU, S.-J. (2010) · International Journal of Modern Physics B · doi:10.1142/s0217979210056335 · Cited by 663
Electronic Structure of Atomically Precise Graphene Nanoribbons
Ruffieux, P., Cai, J., Plumb, N. C., Patthey, L., Prezzi, D., Ferretti, A., Molinari, E., Feng, X., Müllen, K., Pignedoli, C. A., et al. (2012) · ACS Nano · doi:10.1021/nn3021376 · Cited by 494
Metadata
- Authors
- Essler, F. H. L., Frahm, H., Göhmann, F., Klümper, A., & Korepin, V. E.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2005-02-07
- OpenAlex
- W1806543486
- Cited by
- 1,203
- References
- 0
- FWCI
- 8.80
- Type
- book
- Language
- en
- Open access
- closed
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- Essler, F. H. L., Frahm, H., Göhmann, F., Klümper, A., & Korepin, V. E. (2005). The One-Dimensional Hubbard Model. Cambridge University Press eBooks. https://doi.org/10.1017/cbo9780511534843
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