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

Yi-Cong Yu, Y. M. Li, Cv Al

Published Jan 1, 1994• 1 citation

Abstract

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 non-Fermi-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

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

Yi-Cong Yu, Y. M. Li, Cv Al

Published Jan 1, 1994• 1 citation

OpenAlex

Abstract

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BOSONIZATION FOR 2D INTERACTING FERMION SYSTEMS: NON-FERMI LIQUID BEHAVIOR

Y. YU, Y.M. LI, N. d’AMBRUMENIL

arXiv:cond-mat/9401018Modern Physics Letters BJan 10, 19941 citation

Non-Fermi-liquid behavior in two dimensions due to long-ranged current-current interactions

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A. Houghton, John Bradley Marston

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arXiv:cond-mat/9210007Physical review. B, Condensed matterSep 15, 1993186 citations

{\mathit{p}}_{\mathit{F}}

{)}^{3/2}

proposed by Halperin et al. Application of the recent Haldane scheme of bosonization in higher dimensions to this state leads to coupling between bosons, which has the form required for a breakdown of the Landau Fermi-liquid behavior. A generalized form of the Luttinger liquid is obtained.

d

dimensions that diverge in Fourier space for small momentum transfers |q| as $|\mathbf{q}{|}^{\ensuremath{-}\ensuremath{\eta}}$ with $\ensuremath{\eta}=2(d\ensuremath{-}1).$ In this case the single-particle Green's function shows Luttinger-liquid behavior. However, in contrast to

d=1,

in higher dimensions the singularity of the momentum distribution

{n}_{\mathbf{k}}

for wave vectors k close to the Fermi wave vector

{k}_{F}

is characterized by a different exponent than the singularity of the density of states \ensuremath{\rho}(\ensuremath{\omega}) for frequencies \ensuremath{\omega} close to zero. We also calculate the irreducible polarization ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\mathbf{q},\ensuremath{\omega})$ for $|\mathbf{q}|\ensuremath{\approx}{2k}_{F}.$ Whereas in the one-dimensional Tomonaga-Luttinger model ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\ifmmode\pm\else\textpm\fi{}{2k}_{F}+q,\ensuremath{\omega})$ exhibits anomalous scaling, we show that in

d>1

the leading singular corrections cancel. Thus, even though singular density-density interactions in

d>1

lead to Luttinger liquid behavior of the single-particle Green's function, gauge invariant correlation functions such as the polarization or the conductivity show conventional Fermi-liquid behavior. We discuss consequences for the effect of disorder on higher-dimensional Luttinger liquids.

{\mathrm{v}}_{\mathrm{F}}

{\mathrm{k}}_{\mathrm{F}}

/\ensuremath{\lambda}. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent \ensuremath{\alpha} parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)\ensuremath{\sim}1/|p${\mathrm{|}}^{\mathrm{\ensuremath{\alpha}}}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.

{\mathit{T}}^{3}

ln(T) contribution to the specific heat due to small-angle scattering processes. We conclude with a discussion of our results and some speculation about future possibilities.