z = 3 antiferromagnetic quantum critical point : U(1) slave-fermion theory of Anderson lattice model
We find the dynamical exponent $z = 3$ antiferromagnetic (AF) quantum critical point (QCP) in the heavy fermion quantum transition beyond the standard framework of the Hertz-Moriya-Millis theory with $z = 2$. Based on the U(1) slave-fermion representation of the Anderson lattice model, we show the continuous transition from an antiferromagnetic metal to a heavy fermion Fermi liquid, where the heavy fermion phase consists of two fluids, differentiated from the slave-boson theory. Thermodynamics and transport of the $z = 3$ AF QCP are shown to be consistent with the well known non-Fermi liquid physics such as the divergent Grüneisen ratio with an exponent 2/3 and temperature-linear resistivity. In particular, the uniform spin susceptibility turns out to diverge with an exponent 2/3, the hallmark of the $z = 3$ AF QCP described by deconfined bosonic spinons.