Dynamical kinetic energy quenching in antiferromagnetic quantum critical metals

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 on earlier works on the O(3) symmetric theory. The interacting theories in 2+1 dimensions are approached from 3+1-dimensional theories in the ε expansion that tunes the codimension of Fermi surface as a control parameter. The low-energy physics of the Z2 and O(2) theories qualitatively differ from each other and also from that of the O(3) theory. The difference is caused by higher-order quantum corrections beyond the one-loop order that are important even to the leading order in ε. The naive loop expansion breaks down due to dynamical quenching of kinetic energy: the speed of the collective mode (c) and the Fermi velocity perpendicular to the magnetic ordering vector (v) become vanishingly small at low energies. What sets the three theories apart is the hierarchy that emerges between the quenched kinetic terms. At the infrared fixed point, c/v becomes 0, 1, and ∞ in the Z2, O(2), and O(3) theories, respectively. At intermediate energy scales, the slow renormalization group (RG) flows of c and v toward their fixed point values create approximate scale invariance controlled by approximate marginal parameters. The manifold of those quasifixed points and the RG flow therein determines crossovers from scaling behaviors with transient critical exponents at intermediate energy scales to the universal scaling in the low-energy limit. If the symmetry group is viewed as a tuning parameter, then the O(2) theory corresponds to a multicritical point which has one additional quasimarginal parameter than the other two theories.