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

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 2d 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 non-perturbative nature of the theory also shows up in correlation functions of gauge invariant operators.

14 pages, 20 figures; v2) Sec. V on correlation function of gauge invariant operators added; v3) typos corrected, minor changes (to appear in PRB)

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• Quantum Criticality in Heavy Fermion Metals
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• Amperean Pairing Instability in the U(1) Spin Liquid State with Fermi Surface and Application to $\kappa -(BEDT-TTF{)}_{2}C{u}_2(CN{)}_3$
• Algebraic charge liquids
• D-wave correlated Critical Bose Liquids in two dimensions
• Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions
• Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid
• Destruction of Neel order in the cuprates by electron-doping
• Renormalization Group Approach to Strong-Coupled Superconductors
• Fermionic propagators for 2D systems with singular interactions

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