Abstract
We consider an isotropic Fermi liquid in two dimensions near the Pomeranchuk instability in the charge channel. The order parameter is a quadrupolar stress tensor with two bosonic shear modes with polarizations longitudinal and transverse to the quadrupolar momentum tensor. Longitudinal and transverse bosonic modes are characterized by dynamical exponents and , respectively. Previous studies have found that such a system exhibits multiscale quantum criticality with two different energy scales , where is the correlation length. We study the impact of the multiple energy scales on the electron Green’s function. The interaction with the critical mode is known to give rise to a local self-energy that develops a non-Fermi-liquid form, for frequencies larger than the energy scale . We find that the exchange of transverse fluctuations leads to logarithmically singular renormalizations of the quasiparticle residue and the vertex . We derive and solve renormalization-group equations for the flow of and , 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 and varying has a non-Lorentzian form. Away from the QCP, we find that the flow of is cut at the energy scale , associated with the dynamics of electrons. The energy scale, , affects the flow of only if one includes into the theory self-interaction of transverse fluctuations.
3 More- Received 12 March 2010
DOI:https://doi.org/10.1103/PhysRevB.81.235105
©2010 American Physical Society