Dynamical exponent of a quantum critical itinerant ferromagnet: A Monte Carlo study

We consider the effect of the coupling between two-dimensional (2D) quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions. A common belief is that near a q=0 ferromagnetic transition, fermions induce an ω/q Landau damping of rotors (i.e., the dynamical critical exponent is z=3) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy ς∝ω2/3. This behavior has been confirmed in previous quantum Monte Carlo (QMC) studies. Here we show that for the XY case the behavior is different. We report the results of large-scale quantum Monte Carlo simulations, which show that at small frequencies z=2 and ς∝ω1/2. We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces 1/q in the Landau damping by a constant. We discuss the implication of these results to experiments.