The spin density wave quantum phase transition in two dimensional metals

The mean-field theory for the onset of spin density wave order in a metal describes a quantum phase transition which reconstructs the ``large'' Fermi surface to small Fermi pockets. Fluctuations near this transition are described by a quantum field theory of fermions near the reconstruction points, and the bosonic order parameter. This field theory is shown to be strongly-coupled in two spatial dimensions. We find an instability near the quantum critical point to $d$-wave pairing: this is a ``log-squared'' instability, stronger than the familiar logarithmic BCS instability. A similar instability is also found towards a modulated bond order. We also discuss an alternative route for the onset of spin density wave order, via intermediate non-Fermi liquid phases which have small Fermi pockets but without long-range spin density wave order.\\ ~\\ M. A. Metlitski and S. Sachdev, Physical Review B {\bf 82}, 075128 (2010)\\ S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu, Physical Review B {\bf 80}, 155129 (2009)