Correlation functions of higher-dimensional Luttinger liquids

TL;DR

This paper extends the concept of Luttinger liquids to higher dimensions using bosonization, analyzing correlation functions and showing that their scaling behavior differs from one-dimensional cases, with implications for disorder effects.

Contribution

It introduces a higher-dimensional bosonization approach to study Luttinger liquid behavior, revealing complex scaling without a single anomalous exponent.

Findings

Single-particle Green's function exhibits Luttinger liquid behavior in higher dimensions.

Scaling behavior cannot be described by a single anomalous exponent in d>1.

Leading singularities in polarization cancel near 2k_F.

Abstract

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 for small momentum transfers as q^{- eta} with eta = 2 (d-1). In this case the single-particle Green's function shows Luttinger liquid behavior. We discuss the momentum distribution and the density of states and show that, in contrast to d=1, in higher dimensions the scaling behavior cannot be characterized by a single anomalous exponent. We also calculate the irreducible polarization for q close to 2 k_F and show that the leading singularities cancel. We discuss consequences for the effect of disorder on higher-dimensional Luttinger liquids.