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 Omega/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 Sigma proportional to omega(2/3). 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 Sigma proportional to omega(1/2). 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.

Automated summary

In this study, we investigate the effect of the coupling between two-dimensional quantum rotors and itinerant fermions near an XY ferromagnetic quantum critical point. Through large-scale quantum Monte Carlo simulations, we find that the behavior in the XY case is different from previous understanding, with a dynamical critical exponent of 2 and a fermionic self-energy proportional to the square root of frequency. This new behavior is attributed to the fact that a fermionic spin is not a conserved quantity due to spin-spin coupling to rotors. These results have significant implications for experiments.