Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions

Sung-Sik Lee
Phys. Rev. B 80, 165102 – Published 1 October 2009

Abstract

We study the low-energy effective theory for a non-Fermi-liquid state in 2+1 dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with N flavors of fermion in the large N limit. In the low-energy limit, quantum corrections are classified according to the genus of the two-dimensional surface on which Feynman diagrams can be drawn without a crossing in a double line representation and all planar diagrams are important in the leading order. The emerging theory has the similar structure to the four-dimensional SU(N) gauge theory in the large N limit. Because of strong quantum fluctuations caused by the abundant low-energy excitations near the Fermi surface, low-energy fermions remain strongly coupled even in the large N limit. As a result, there are infinitely many quantum corrections that contribute to the leading frequency dependence of the Green’s function of fermion on the Fermi surface. On the contrary, the boson self-energy is not modified beyond the one-loop level and the theory is stable in the large N limit. The nonperturbative nature of the theory also shows up in correlation functions of gauge-invariant operators.

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  • Received 16 June 2009

DOI:https://doi.org/10.1103/PhysRevB.80.165102

©2009 American Physical Society

Authors & Affiliations

Sung-Sik Lee

  • Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1

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Issue

Vol. 80, Iss. 16 — 15 October 2009

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