Fermionic propagators for 2D systems with singular interactions

Abstract

We analyze the form of the fermionic propagator for 2D fermions interacting with massless overdamped bosons. Examples include a nematic and Ising ferromagnetic quantum-critical points, and fermions at a half-filled Landau level. Fermi liquid behavior in these systems is broken at criticality by a singular self-energy, but the Fermi surface remains well defined. These are strong-coupling problems with no expansion parameter other than the number of fermionic species, N. The two known limits, N >>1 and N=0 show qualitatively different behavior of the fermionic propagator G(ε_k, ω). In the first limit, G(ε_k, ω) has a pole at some ε_k, in the other it is analytic. We analyze the crossover between the two limits. We show that the pole survives for all N, but at small N it only exists in a range O(N^2) near the mass shell. At larger distances from the mass shell, the system evolves and G(ε_k, ω) becomes regular. At N=0, the range where the pole exists collapses and G(ε_k, ω) becomes regular everywhere.

16 twocolumn pages, 3 figures, submitted to PRB

References in corpus (14)

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• Electrical resistivity near Pomeranchuk instability in two dimensions
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• Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases
• Pairing Instability in a Nematic Fermi Liquid
• Breakup of a Stoner model for the 2D ferromagnetic quantum critical point
• The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions

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• Gauge-field fluctuations in 3D topological Mott insulators
• Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals
• Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
• Is the composite fermion state of Graphene a doped Chern insulator?
• Two-point function of a $d=2$ quantum critical metal in the limit $k_F\to \infty$, $N_f\to 0$ with $N_f{k}_F$ fixed
• Cavity-Vacuum-Induced Chiral Spin Liquids in Kagome Lattices: Tuning and Probing Topological Quantum Phases via Cavity Quantum Electrodynamics
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography
• A Framework for Studying a Quantum Critical Metal in the Limit $N_f\to 0$
• Instabilities of quantum critical metals in the limit $N_f\to 0$