Fermi and Luttinger Liquids in Low-Dimensional Metals
The standard description of (three-dimensional) metals is based on the Landau theory of Fermi systems (Fermi Liquid theory) . Within this theory all low-energy and low- temperature properties are described in terms of independent elementary excitations (quasi- particles) which behave more or less as free particles. This picture breaks down in one dimensional systems, which are instead described by the so called Luttinger Liquid theory . Indeed experimental evidence suggests that Fermi Liquid theory could break down in a variety of physical situations.
KeywordsAnisotropy Helium Compressibility Haldane
Unable to display preview. Download preview PDF.
- 1a.See for instance: P. Nozières, “Theory of interacting Fermi Systems” (Benjamin, 1964);Google Scholar
- 1b.G.Baym and C. Pethick in “The physics of liquid and solid Helium”, ed. Bennemann and Ketterson (Wiley, 1978)Google Scholar
- 4.All energies are measured with respect to the Fermi energy.Google Scholar
- 9.I. E. Dzyaloshinskii and A.I. Larkin, Sov. Phys. JETP 38, 202 (1974).Google Scholar
- 12.C. Bourbonnais in “Highly correlated fermion systems and high Tc superconductors” ed. B. Douçot and R.Rammal (Elsevier, 1991)Google Scholar
- 13.H.J.Schulz, “The metal-insulator transition in one dimension”, in “Strongly correlated electronic materials: the Los Alamos Symposium 1993”, ed. K.S. Bedell et al. (Addison-Wesley, 1994)Google Scholar
- 15.A detailed discussion of the role of conservation laws in deriving these equations is given by W. Metzner and C.Di Castro, Phys Rev. B 47, 16107 (1993)Google Scholar
- 16.Notice that eq.(14) has the suggestive form of a gauge transformation: because of eq.(13), the interactions have been gauged out apart from anomalies leading to the RPA “gauge field”.Google Scholar
- 17b.C.Bourbonnais and L.G.Caron, ibidem B 5, 1033 (1991);Google Scholar
- 17d .
- 17e.M.Fabrizio, ibidem B 48, 15838 (1993).Google Scholar
- 19.Note that the perturbation theory in 1<d<2 shows indeed the asymptotic dominance of the forward scattering we are considering .Google Scholar
- 21.C.Castellani, C. Di Castro and A.Maccarone, unpublished.Google Scholar