Luttinger liquid

A Luttinger liquid, or Tomonaga–Luttinger liquid, is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor (e.g. quantum wires such as carbon nanotubes).^[1] Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension.

The Tomonaga–Luttinger's liquid was first proposed by Sin-Itiro Tomonaga in 1950. The model showed that under certain constraints, second-order interactions between electrons could be modelled as bosonic interactions. In 1963, J.M. Luttinger reformulated the theory in terms of Bloch sound waves and showed that the constraints proposed by Tomonaga were unnecessary in order to treat the second-order perturbations as bosons. But his solution of the model was incorrect; the correct solution was given by Daniel C. Mattis [de] and Elliot H. Lieb 1965.^[2]

^ Blumenstein, C.; Schäfer, J.; Mietke, S.; Meyer, S.; Dollinger, A.; Lochner, M.; Cui, X. Y.; Patthey, L.; Matzdorf, R.; Claessen, R. (October 2011). "Atomically controlled quantum chains hosting a Tomonaga–Luttinger liquid". Nature Physics. 7 (10): 776–780. Bibcode:2011NatPh...7..776B. doi:10.1038/nphys2051. ISSN 1745-2473.
^ Mattis, Daniel C.; Lieb, Elliot H. (February 1965). Exact solution of a many-fermion system and its associated boson field. Vol. 6. pp. 98–106. Bibcode:1994boso.book...98M. doi:10.1142/9789812812650_0008. ISBN 978-981-02-1847-8. {{cite book}}: |journal= ignored (help)

[1] Blumenstein, C.; Schäfer, J.; Mietke, S.; Meyer, S.; Dollinger, A.; Lochner, M.; Cui, X. Y.; Patthey, L.; Matzdorf, R.; Claessen, R. (October 2011). "Atomically controlled quantum chains hosting a Tomonaga–Luttinger liquid". Nature Physics. 7 (10): 776–780. Bibcode:2011NatPh...7..776B. doi:10.1038/nphys2051. ISSN 1745-2473.

[2] Mattis, Daniel C.; Lieb, Elliot H. (February 1965). Exact solution of a many-fermion system and its associated boson field. Vol. 6. pp. 98–106. Bibcode:1994boso.book...98M. doi:10.1142/9789812812650_0008. ISBN 978-981-02-1847-8. {{cite book}}: |journal= ignored (help)

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