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arXiv:cond-mat/9405083 · Physical review. B, Condensed matter

Gauge-invariant response functions of fermions coupled to a gauge field

Yong Baek Kim, Akira Furusaki, Xiao-Gang Wen, Patrick A. Lee

Published Dec 15, 1994• 204 citations
arXivHTMLPDF

Abstract

We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be canceled by those from the vertex correction for small q and \ensuremath{\Omega}. As a result, the remaining contributions are not singular enough to change the leading-order results of the random-phase approximation. It is also shown that the gauge-field propagator is not renormalized up to two-loop order. We examine the resulting gauge-invariant two-particle Green's functions for small q and \ensuremath{\Omega}, but for all ratios of \ensuremath{\Omega}/${\mathit{v}}_{\mathit{F}}$q, and we conclude that they can be described by Fermi-liquid forms without a diverging effective mass.

DOI
10.1103/physrevb.50.17917

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We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be canceled by those from the vertex correction for small q and \ensuremath{\Omega}. As a result, the remaining contributions are not singular enough to change the leading-order results of the random-phase approximation. It is also shown that the gauge-field propagator is not renormalized up to two-loop order. We examine the resulting gauge-invariant two-particle Green's functions for small q and \ensuremath{\Omega}, but for all ratios of \ensuremath{\Omega}/vF{\mathit{v}}_{\mathit{F}}vF​q, and we conclude that they can be described by Fermi-liquid forms without a diverging effective mass.
We calculate the fermion Green function and particle-hole susceptibilities for a degenerate two-dimensional fermion system with a singular gauge interaction. We show that this is a strong-coupling problem, with no small parameter other than the fermion spin degeneracy N. We consider two interactions, one arising in the context of the t-J model and the other in the theory of half-filled Landau level. For the fermion self-energy we show that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{Q}}$ at a general wave vector Q\ensuremath{\ne}2pF{\mathbf{p}}_{\mathbf{F}}pF​ retains the Fermi-liquid form. However, the 2pF{\mathit{p}}_{\mathit{F}}pF​ susceptibility ${\mathrm{\ensuremath{\chi}}}_{2\mathit{p}\mathit{F}}$ either diverges as T\ensuremath{\rightarrow}0 or remains finite but with nonanalytic wave-vector, frequency, and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in d=2, but irrelevant at low energies in d\ensuremath{\ge}2.
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