Bosonization for 2D Interacting Fermion Systems: Non-Fermi Liquid Behavior

Non-Fermi liquid behavior is found for the first time in a two-dimensional (2D) system with non-singular interactions using Haldane’s bosonization scheme. The bosonized system is solved exactly by a generalized Bogoliubov transformation. The fermion momentum distribution, calculated using a generalized Mattis-Lieb technique, exhibits a non-universal power law in the vicinity of the Fermi surface for intermediate interaction strengths. In recent years, there has been great interest in possible non-Fermi-liquid-like behavior in the ground state of two-dimensional (2D) strongly correlated fermionic systems [1]. It is well-known that in one dimension the ground state of a fermionic system with arbitrarily weak interactions is not a Fermi liquid but a state usually known as a Luttinger liquid [2]. For the 2D case, many studies have suggested that, in the limit of weak interactions, this behavior does not appear [3]. Studies of systems with a small number of particles also suggest Fermi liquid behavior in 2D [4]. Although Khveshchenko et al have found nonFermi-liquid behavior in 2D, they worked only with a singular long-range current-current interaction [5]. The one-dimensional Luttinger liquid solution can be obtained by a bosonization procedure [2]. Haldane has recently generalized this procedure to solve 2D models [6] and his method has been further developed in [5]. In this paper, we show using this procedure that, even for non-singular short-range interactions, 2D systems may show non-Fermi-liquid behavior if the interaction is strong enough. However, in the limit of weak interactions it is difficult to distinguish between a Fermi liquid and a non-Fermi liquid. We diagonalize the bosonized model exactly using a generalized Bogoliubov transformation. The fermion momentum distribution n(p) at zero temperature is then calculated using a generalization to higher dimensions of the method used by Mattis and Lieb [7] in 1D. The power law obtained in 1D for n(p) near pF , n(p) ∼ (p − pF ), also emerges in 2D. The exponents, δ, can be calculated numerically. We look in particular at the case of a δ-function interaction and find that the variation of δ with coupling constant is similar to that found in 1D, although δ is always smaller in 2D than 1D for comparable values of the coupling constants.