Field Theories of Quantum Critical Metals

In certain metals, a phase transition occurs at zero (absolute) temperature as another parameter is varied- the point of transition is know as a Quantum Critical Point (QCP). A quantum critical phase may then "fan out" from the QCP into the 2-D parameter space (in particular, to nonzero T). Metals in this unstable, exotic phase may have novel experimental properties, like power-law dependence of resistivities on temperature persisting over a large range or a divergent Sommerfeld coefficient- furthermore, existing theoretical descriptions not only fail to reproduce these features, they also suffer some serious fundamental inconsistencies which call into question their applicability. In this project, I hope to address these theoretical flaws by formulating a logically consistent theory of these metals, in particular utilizing and developing renormalization group approaches which explicitly treat both the fermions and bosons of the system (in contrast to Hertz-Millis theory [1,2], which "integrates out" the fermions). In a nonrelativistic theory, fermion and boson renormalization are quite different procedures- bosonic momenta, free from the Pauli Principle, are "shrunk" to the origin, while for fermions the cutoff is imposed about the Fermi surface. There is thus the unanswered question of which flow parameter to use for a unified RG treatment of a fermion-boson system, which may not simply be answerable by "picking" some parameter or another, but perhaps instead by a fundamental reformulation of our approach. I intend to investigate this and other lines of inquiry in an effort to improve our theoretical understanding of quantum criticality in metals.