Abstract
In one dimension, interacting systems of fermions show behavior very different from that of usual Fermi liquids. The properties of such systems can be discussed in a rather simple way based on the bosonization technique. The most interesting features that arise are the separation of the dynamics of the spin and charge degrees of freedom and the appearance of non-universal (i.e. interaction-dependent) laws in the low-energy and long-wavelength properties (“ Luttinger liquid”). The consequences of these phenomena for different physical properties (transport, NMR relaxation time, spectral functions,…) are described, with emphasis on the vicinity of the metal-insulator transition. The problems arising if one tries to generalize this type of behavior to more than one dimension are discussed.
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