Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order

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 z receives corrections to its mean-field value z = 2. At higher orders in the loop expansion, we find infrared singularities similar to those found by S.-S. Lee for the problem of a Fermi surface coupled to a gauge field. A treatment of these singularities implies that an expansion in 1/N, (where N 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.

59 pages, 23 figures; (v2) added clarifications

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• Instabilities near the onset of spin density wave order in metals
• Quantum critical point shifts under superconductivity: the pnictides and the cuprates
• Quantum criticality of reconstructing Fermi surfaces in antiferromagnetic metals
• Nambu-Eliashberg theory for multi-scale quantum criticality : Application to ferromagnetic quantum criticality in the surface of three dimensional topological insulators
• Critical particle-hole composites at twice the Fermi wave vector in U(1) spin liquid with a Fermi surface