Abstract
We present a field-theoretic renormalization group analysis of Abanov and Chubukov’s model of the spin density wave transition in two dimensional metals. We identify the independent field scale and coupling constant renormalizations in a local field theory and argue that the damping constant of spin density wave fluctuations tracks the renormalization of the local couplings. The divergences at two-loop order overdetermine the renormalization constants and are shown to be consistent with our renormalization scheme. We describe the physical consequences of our renormalization-group equations, including the breakdown of Fermi liquid behavior near the “hot spots” on the Fermi surface. In particular, we find that the dynamical critical exponent receives corrections to its mean-field value . At higher orders in the loop expansion, we find infrared singularities similar to those found by Lee [Phys. Rev. B 80, 165102 (2009)] for the problem of a Fermi surface coupled to a gauge field. A treatment of these singularities implies that an expansion in (where is the number of fermion flavors) fails for the present problem. We also discuss the renormalization of the pairing vertex and find an enhancement which scales as logarithm squared of the energy scale. A similar enhancement is also found for a modulated bond order which is locally an Ising-nematic order.
16 More- Received 2 May 2010
DOI:https://doi.org/10.1103/PhysRevB.82.075128
©2010 American Physical Society
Viewpoint
Hidden one-dimensional physics in 2D critical metals
Published 16 August 2010
New theoretical work shows that in two-dimensional condensed matter systems, one-dimensional processes such as forward or backward scattering have a dramatic effect on the physical behavior of fermions near a quantum critical point and derail attempts to get an accurate description of a non-Fermi-liquid.
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