Journal
PHYSICAL REVIEW B
Volume 80, Issue 16, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.80.165102
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Funding
- NSERC
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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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