A new bosonisation procedure based on an exact method of functional integration is applied to the one-dimensional Tomonaga (1950)-Luttinger (1963) model with forward scattering. This method circumvents the conventional procedure where the fermion field operator is represented by (bosonic) charge and spin density fields. Fictitious auxiliary fields are introduced to deal with the interaction term so that the fermionic degrees of freedom can be integrated out exactly. In addition to the usual description of the system in terms of charge and spin fluctuations, an effective action in terms of the auxiliary fields can be used. The evaluation of the Green function is facilitated if the latter route is taken. The authors' results for the spinless and spin-1/2 cases agree with previous work.
Using higher-dimensional bosonization we study correlation functions of fermions with singular forward scattering. Following Bares and Wen [Phys. Rev. B 48, 8636 (1993)] we consider density-density interactions in
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
nk for wave vectors k close to the Fermi wave vector
kF 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.
The one-particle Green's function for the two-chain Tomonaga–Luttinger (TL) model coupled by interchain hopping including spin degrees of freedom is calculated as a function of distance and time by the higher-dimensional bosonization method. In the short distance and time region, the one-dimensional TL liquid behavior is reproduced, while the long distance and time behavior is different from that for either TL or Fermi liquid. As the interaction becomes stronger, the behavior of Green's function becomes closer to that for the one-dimensional TL liquid, showing that the one-dimensionality is enhanced for stronger electron interaction, and is interpreted as the precursor of the “confinement”.
We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition.