2010/05/31 by Markus Garst, Andrey V. Chubukov
Materials Science · Physics and Astronomy · #Condensed matter physics #Critical exponent #Electron #Fermi liquid theory #Mathematical physics #Omega #Order (exchange) #Organic and Molecular Conductors Research #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum critical point #Quantum mechanics #Quantum phase transition #Quasiparticle #Superconductivity #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.81.235105
published as Phys.Rev.B81:235105,2010 · 14 pages, 10 figures; (v2) minor changes, published version
openalex publication_date 2010/06/07 · arxiv created 2010/07/16 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 bosonic shear modes with polarizations longitudinal and transverse to the quadrupolar momentum tensor. Longitudinal and transverse bosonic modes are characterized by dynamical exponents z_\ensuremath∥=3 and z_\ensuremath⊥=2, respectively. Previous studies have found that such a system exhibits multiscale quantum criticality with two different energy scales \ensuremathω\ensuremath∼\ensuremathξ^\ensuremath-z_\ensuremath∥,\ensuremath⊥, where \ensuremathξ is the correlation length. We study the impact of the multiple energy scales on the electron Green's function. The interaction with the critical z_\ensuremath∥=3 mode is known to give rise to a local self-energy that develops a non-Fermi-liquid form, \ensuremathΣ(\ensuremathω)\ensuremath∼\ensuremathω2/3 for frequencies larger than the energy scale \ensuremathω\ensuremath∼\ensuremathξ^\ensuremath-3. We find that the exchange of transverse z_\ensuremath⊥=2 fluctuations leads to logarithmically singular renormalizations of the quasiparticle residue Z and the vertex \ensuremathΓ. We derive and solve renormalization-group equations for the flow of Z and \ensuremathΓ, 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 \ensuremathω 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 \ensuremathωFL\ensuremath∝\ensuremathξ^\ensuremath-1, associated with the z=1 dynamics of electrons. The z_\ensuremath⊥=2 energy scale, \ensuremathω\ensuremath∼\ensuremathξ^\ensuremath-2, affects the flow of Z only if one includes into the theory self-interaction of transverse fluctuations.