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Luttinger Liquids With and Without Using Sea-Bosons

By Girish S. Setlur


The last and important deficiency of the sea-boson method namely its apparent inability to allow for Luttinger liquids is resolved. We solve the Luttinger model and compute the anomalous exponents. As it happens, this exercise is diabolically subtle, much more so because we can compute the momentum distribution directly without computing the propagator. We also compute the full propagator of this model using just Fermi algebra that pays attention to fluctuations in the momentum distribution. We then apply the sea-boson technique to solve the Calogero Sutherland model and find that here too we have a Luttinger liquid and compute the anomalous exponents. The main advantage of the sea-boson approach is its ability to provide information about short-wavelength physics in addition to the asymptotics and that too without necessarily consciously invoking momentum cutoffs, anomalous commutators and the like. All these methods are naturally generalizable to more than one dimension.

Year: 2008
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