Comments on Large-N theory of Critical Fermi Surfaces

Critical Fermi surfaces appear in many physical systems, including the half-filled Landau level, and certain spin liquids. Many theories have studied the nonquasiparticle excitations near the Fermi surface, and possible instabilities to pairing or density wave orders, but without a fully systematic method. Here, the authors study an ensemble of self-averaging theories with random coupling constants, and obtain a controlled large- $N$ expansion.Critical Fermi surfaces appear in many physical systems, including the half-filled Landau level, and certain spin liquids. Many theories have studied the nonquasiparticle excitations near the Fermi surface, and possible instabilities to pairing or density wave orders, but without a fully systematic method. Here, the authors study an ensemble of self-averaging theories with random coupling constants, and obtain a controlled large-$N$ expansion.

arXiv:2103.08615Physical review. B./Physical review. BJun 14, 2021103 citations

Large- N theory of critical Fermi surfaces. II. Conductivity

Haoyu Guo, Aavishkar A. Patel, Ilya Esterlis +1 more

A Fermi surface coupled to a scalar field can be described in a $1/N$ expansion by choosing the fermion-scalar Yukawa coupling to be random in the $N$ -dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and verify that the proposed $1/{\ensuremath{\omega}}^{2/3}$ contribution to the optical conductivity at frequency $\ensuremath{\omega}$ has vanishing coefficient for a convex Fermi surface. We also describe the influence of impurity scattering of the fermions, and find that while the self-energy resembles a marginal Fermi liquid, the resistivity and optical conductivity behave like a Fermi liquid.A Fermi surface coupled to a scalar field can be described in a $1/N$ expansion by choosing the fermion-scalar Yukawa coupling to be random in the $N$-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and verify that the proposed $1/{\ensuremath{\omega}}^{2/3}$ contribution to the optical conductivity at frequency $\ensuremath{\omega}$ has vanishing coefficient for a convex Fermi surface. We also describe the influence of impurity scattering of the fermions, and find that while the self-energy resembles a marginal Fermi liquid, the resistivity and optical conductivity behave like a Fermi liquid.

arXiv:2207.08841Physical review. B./Physical review. BSep 30, 202271 citations

Fermions and the Fermi surface

Lecture notes in physics. M, MonographsJan 1, 19970 citations

On Large Densities in Fermi Systems

A. A. Zamyatin, V. A. Malyshev

Mathematical NotesNov 1, 20050 citations

N

expansion.

A Fermi surface coupled to a scalar field can be described in a

1/N

expansion by choosing the fermion-scalar Yukawa coupling to be random in the

N

-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and verify that the proposed $1/{\ensuremath{\omega}}^{2/3}$ contribution to the optical conductivity at frequency $\ensuremath{\omega}$ has vanishing coefficient for a convex Fermi surface. We also describe the influence of impurity scattering of the fermions, and find that while the self-energy resembles a marginal Fermi liquid, the resistivity and optical conductivity behave like a Fermi liquid.