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Series on directions in condensed matter physics

LUTTINGER MODEL IN DIMENSIONS d > 1

Daniel Charles Mattis

Published Oct 24, 2013• 0 citations
Publisher
DOI
10.1142/9789814520720_0013

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International Journal of Modern Physics B•Jul 26, 2012•1 citation
The instabilities induced on a two-dimensional system of correlated electrons by the anisotropies of its Fermi line are analyzed on general grounds. Simple scaling arguments allow to predict the opening of a superconducting gap with a well-defined symmetry prescribed by the geometry of the Fermi line. The same arguments predict a critical dimension of 3/2 for the transition of the two-dimensional system to non-Fermi liquid behavior. The methods are applied to the t–t′ Hubbard model in a wide range of dopings.
The Luttinger model owes its solvability to a number of peculiar features, like its linear relativistic dispersion relation, which are absent in more realistic fermionic systems. Nevertheless according to the Luttinger liquid conjecture a number of relations between exponents and other physical quantities, which are valid in the Luttinger model, are believed to be true in a wide class of systems, including tight binding or jellium one-dimensional fermionic systems. Recently a rigorous proof of several Luttinger liquid relations in nonsolvable models has been achieved; it is based on exact Renormalization Group methods coming from Constructive Quantum Field Theory and its main steps will be reviewed below.
The Luttinger model owes its solvability to a number of peculiar features, like its linear relativistic dispersion relation, which are absent in more realistic fermionic systems. Nevertheless according to the Luttinger liquid conjecture a number of relations between exponents and other physical quantities, which are valid in the Luttinger model, are believed to be true in a wide class of systems, including tight binding or jellium one-dimensional fermionic systems. Recently a rigorous proof of several Luttinger liquid relations in nonsolvable models has been achieved; it is based on exact Renormalization Group methods coming from Constructive Quantum Field Theory and its main steps will be reviewed below.