Electron self-energy near a nematic quantum critical point
Abstract
We consider an isotropic Fermi liquid in two dimensions near the n=2 Pomeranchuk instability in the charge channel. The order parameter is a quadrupolar stress tensor with two polarizations, longitudinal and transverse to the quadrupolar momentum tensor. Longitudinal and transverse bosonic modes are characterized by dynamical exponents zparallel=3 and zperp=2, respectively. Previous studies have found that such a system exhibits multiscale quantum criticality with two different energy scales omega ~ xi-zparallel,perp, where xi is the correlation length. We study the impact of the multiple energy scales on the electron Green function. The interaction with the critical zparallel =3 mode is known to give rise to a local self-energy that develops a non-Fermi liquid form, Sigma(omega) ~ omega2/3 for frequencies larger than the energy scale omega ~ xi-3. We find that the exchange of transverse zperp=2 fluctuations leads to a logarithmically singular renormalizations of the quasiparticle residue Z and the vertex Gamma. We derive and solve renormalization group equations for the flow of Z and Gamma and show that the system develops an anomalous dimension at the nematic quantum-critical point (QCP). As a result, the spectral function at a fixed omega and varying k has a non-Lorentzian form. Away from the QCP, we find that the flow of Z is cut at the energy scale omegaFL ~ xi-1, associated with the z=1 dynamics of electrons. The zperp=2 energy scale, omega ~ xi-2, affects the flow of Z only if one includes into the theory self-interaction of transverse fluctuations.