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arXiv:0901.1459 · Physical Review B

Fermionic propagators for two-dimensional systems with singular interactions

Tigran Sedrakyan, Andrey V. Chubukov

Published Mar 25, 2009• 24 citations
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Abstract

We analyze the form of the fermionic propagator for two-dimensional 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 $G({ϵ}_{k},\ensuremath{\omega})$. In the first limit, $G({ϵ}_{k},\ensuremath{\omega})$ 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 $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular. At $N=0$, the range where the pole exists collapses and $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular everywhere.

DOI
10.1103/physrevb.79.115129

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