Non-Relativistic Fermions Coupled to Transverse Gauge-Fields: The Single-Particle Green's Function in Arbitrary Dimension

Abstract

We use a bosonization approach to calculate the single-particle Green's function $G(\mathbf{r},\tau )$ of non-relativistic fermions coupled to transverse gauge-fields in arbitrary dimension $d$. We find that in $d>3$ transverse gauge-fields do not destroy the Fermi liquid, although for $d<6$ the quasi-particle damping is anomalously large. For $d\to 3$ the quasi-particle residue vanishes as $Z\propto \exp [-\frac{1}{2\pi (d-3)}(\frac{\kappa }{mc}{)}^2]$, where $\kappa$ is the Thomas-Fermi wave-vector, $m$ is the mass of the electrons, and $c$ is the velocity of the gauge-particle. In $d=3$ the system is a Luttinger liquid, with anomalous dimension ${\gamma }_{\perp }=\frac{1}{6\pi }(\frac{\kappa }{mc}{)}^2$. For $d<3$ we find that $G(\mathbf{r},0)$ decays exponentially at large distances.

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Cited by in corpus (5)

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• Quasi-particle behavior of composite fermions in the half-filled Landau level
• Correlation functions of higher-dimensional Luttinger liquids
• Vertex corrections in gauge theories for two-dimensional condensed matter systems