Topological Electronic Liquids Electronic Physics of One Dimension Beyond the One Dimension

There is a class of electronic liquids in dimensions greater than one, which show all essential properties of one dimensional electronic physics. These are topological liquids correlated electronic systems with a spectral flow. Compressible topological electronic liquids are superfluids. In this paper we present a study of a conventional model of a topological superfluid in two spatial dimensions. This model is thought to be relevant to a doped Mott insulator. We show how the spectral flow leads to the superfluid hydrodynamics and how the Orthogonality Catastrophe affects off-diagonal matrix elements. We also compute the major electronic correlation functions. Among them are the spectral function, the pair wave function and various tunneling amplitudes. To compute correlation functions we develop a method of current algebra an extension of the bosonization technique of one spatial dimension. In order to emphasize a similarity between electronic liquids in one dimension and topological liquids in dimensions greater than one, we first review the Frohlich-Peierls mechanism of ideal conductivity in one dimension and then extend the physics and the methods into two spatial dimension. The paper is based on the lectures given at Troisième cycle de la physique en Suisse romande EPFL, Lausanne June 1997.