Abstract
A model for interacting spinless fermions in one dimension is solved exactly and later extended to the spin case. The solution is based on a mapping where interactions appear as geometric constraints. It is simple enough to allow a complete Luttinger liquid characterization, including criticality. This geometric interpretation of interactions is shown to be a convenient framework to understand criticality in any Luttinger liquid, and is applied to recover some transport properties in an elementary way.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
See, for instance, M. Gaudin, La fonction d’onde de Bethe (Masson, Paris, 1983).
See, for instance, J. P. Pouget, in Low-Dimensional Conductors and Superconductors, edited by D. Jerome and L. Caron (Plenum, New York, 1987).
V. J. Emery, in Highly Conducting One-Dimensional Solids, edited by J. T. Devreese et al. (Plenum, New York, 1979).
J. Solyom, Adv. Phys. 28, 201 (1979).
P. W. Anderson, Phys. Rev. Lett. 64, 1839 (1990); 65, 2306 (1990).
F. D. M. Haldane, Phys. Rev. Lett. 45, 1358 (1980); 47, 1840 (1981); J. Phys. C 14, 2585 (1981).
D. C. Mattis and E. H. Lieb, J. Math. Phys. 6, 304 (1965).
M. den Nijs, Phys. Rev. B 23, 6111 (1981); also in Phase Transitions and Critical Phenomena, vol. 12 (Academic Press, London, 1988).
G. Gómez-Santos, Phys. Rev. Lett. 70, 3780 (1993).
H. Frahm and V. E. Korepin, Phys. Rev. B 42, 10553 (1990).
P. A. Bares and G. B. Blatter, Phys. Rev. Lett. 64, 2567 (1990)
N. Kawakami and S.-K. Yang, Phys. Rev. Lett. 65, 2309 (1990).
E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968).
J. Villain and P. Bak, J. Physique 42, 657 (1981).
J. Hubbard, Phys. Rev. B 17, 494 (1978).
G. V. Uimin and V. L. Pokrovsky, J. Physique 44, L865 (1983)
L. A. Bol’shov, V. L. Pokrovsky and G. V. Uimin, J. Stat. Phys. 38, 191 (1985).
C. L. Kane and M. P. A. Fisher, Phys. Rev. Lett. 68, 1220 (1992).
M. Ogata and H. Shiba, Phys. Rev. B 41, 2326 (1990)
A. Parola and S. Sorella, Phys. Rev. Lett. 64, 1831 (1990).
H. J. Schulz, Phys. Rev. Lett. 64, 2831 (1990); Int. J. Mod. Phys. B 5, 57 (1991).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gómez-Santos, G. (1995). One-Dimensional Luttinger Liquid of Particles for a Class of Infinitely Repulsive Interactions: Exact Solution. In: Baeriswyl, D., Campbell, D.K., Carmelo, J.M.P., Guinea, F., Louis, E. (eds) The Hubbard Model. NATO ASI Series, vol 343. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1042-4_5
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1042-4_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1044-8
Online ISBN: 978-1-4899-1042-4
eBook Packages: Springer Book Archive