Explaining the behavior of interacting electrons in a solid is one of the long-standing problems in condensed matter. For most systems, the problem has been masterfully addressed by Landau, who showed that even though interactions can be very large, excitations behaving essentially as free fermions still exist in the system. The Landau Fermi-liquid theory allows sweeping the interactions under the rug and saying that the properties of many materials will be very similar to those of free electrons. However, this theory fails spectacularly when an electron gas is confined to one dimension. In that case, a completely new universality class appears, and the Fermi liquid turns into a Luttinger liquid.
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