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

By Sung-Sik Lee. 2009

281 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/be4f57b9e58ea4cadbaa68584f0748d1a895225e

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Hidden Fermi surfaces in compressible states of gauge-gravity duality (2011, background): “This is also the behavior found in recent gauge theories [46, 52–54] of non-Fermi liquid states in d = 2, provided we identify z with the dynamic scaling of the Green’s function of the gauge-charged fermions in the direction normal to the Fermi surface (in Ref.”
Semi-holographic Fermi liquids (2010, background): “A third class of ideas, based on emergent gauge theories, presents the difficulty of understanding the resulting strongly coupled dynamics [3].”
What Can Gauge-Gravity Duality Teach Us about Condensed Matter Physics? (2011, background): “[39] Sung-Sik Lee, “Low energy effective theory of Fermi surface coupled with U(1) gauge field in”
Holographic Quantum Matter (2016, methodology): “The theory SIN has been much studied in the literature by a variety of sophisticated field-theoretic methods [158; 497; 553; 563].”
Electron stars for holographic metallic criticality (2010, unknown): “It has recently been demonstrated [5, 6, 4] that the vector large N expansion breaks down for 2+1 dimensional metallic quantum critical systems.”