The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study

TL;DR

This study uses large-scale quantum Monte Carlo simulations to reveal that a 2D quantum rotor system coupled to itinerant fermions near a ferromagnetic quantum critical point exhibits a dynamical exponent of 2 and a fermionic self-energy proportional to , differing from the previously believed behavior.

Contribution

The paper demonstrates that in the XY ferromagnetic quantum critical case, the dynamical exponent is 2 and fermionic self-energy scales as , challenging the conventional z=3 Landau damping picture.

Findings

At small frequencies, the dynamical exponent is z=2.

Fermionic self-energy scales as  (  ).

The behavior differs from the standard Landau damping theory.

Abstract

We consider the effect of the coupling between 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 $\Sigma\propto \omega^{2/3}$. 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 $\Sigma\propto \omega^{1/2}$. 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.