Low-Energy Effective Field Theories for the Antiferromagnetic Quantum Critical Metal with Z2, O(2) and O(3) spin symmetries

Abstract

In this thesis, we study the low-energy physics of the antiferromagnetic quantum critical metal. In the first part of the thesis, we study the dynamics of critical spin fluctuations and hot electrons at the metallic antiferromagnetic quantum critical points with Z2 and O(2) spin symmetries, building upon earlier works on the O(3) symmetric theory. The interacting theories in 2+1 dimensions are approached from 3 + 1-dimensional theories in the epsilon-expansion that tunes the co-dimension of Fermi surface as a control parameter. Irrespective of the spin symmetry, the theories exhibit emergent kinetic energy quenching as the speed of the collective mode (c) and the Fermi velocity perpendicular to the magnetic ordering vector (v) become vanishingly small at low energies. However, the low-energy physics of the Z2, O(2) and O(3) theories qualitatively differ from each other due to distinct emergent hierarchy between the quenched kinetic terms. At the infrared fixed point, c/v becomes 0, 1 and infinity in the Z2, O(2) and O(3) theories, respectively. The slow renormalization group (RG) flows of c and v to their fixed point values create approximate scale invariance controlled by approximate marginal parameters within finite but large windows of energy scales. The manifold of those quasi-fixed points and the RG flow therein determines crossovers from scaling behaviours with transient critical exponents at intermediate energy scales to the universal scaling in the low-energy limit. In the second part of the thesis, we develop a field-theoretic functional renormalization group formalism for full low-energy effective field theories of non-Fermi liquids that include all gapless modes around the Fermi surface. The formalism is applied to the non-Fermi liquid that arises at the antiferromagnetic quantum critical point in two space dimensions with O(3) symmetry. In the space of coupling functions, an interacting fixed point arises at a point with momentum-independent coupling functions and vanishing v. In theories deformed with non-zero v, coupling functions acquire universal momentum profiles controlled by the bare values of v before flowing to superconducting states in the low-energy limit.