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In previous work we have proposed that the non-Fermi-liquid spectralproperties in a variety of low-dimensional and strongly correlated electronsystems are caused by the infrared catastrophe, and we used an exact functionalintegral representation for the interacting Green's function to map thetunneling problem onto the x-ray edge problem, plus corrections. Thecorrections are caused by the recoil of the tunneling particle, and, in systemswhere the method is applicable, are not expected to change the qualitative formof the tunneling density of states (DOS). Qualitatively correct results wereobtained for the DOS of the 1D electron gas and 2D Hall fluid when thecorrections to the x-ray edge limit were neglected and when the correspondingNozieres-De Dominicis integral equations were solved by resummation of adivergent perturbation series. Here we reexamine the x-ray edge limit for thesetwo models by solving these integral equations exactly, finding the expectedmodifications of the DOS exponent in the 1D case but finding no changes in theDOS of the 2D Hall fluid with short-range interaction. We also provide, for thefirst time, an exact solution of the Nozieres-De Dominicis equation for the 2Delectron gas in the lowest Landau level.Comment: 6 pages, Revte

physical review. b, condensed matter and materials physics

Infrared catastrophe and tunneling into strongly correlated electron systems: Exact x-ray edge limit for the one-dimensional electron gas and two-dimensional Hall fluid