Numerical evidence for unstable magnons at high fields in the Heisenberg antiferromagnet on the square lattice

We find evidence for decaying magnons at strong magnetic field in the square lattice spin-1/2 Heisenberg antiferromagnet. The results are obtained using quantum Monte Carlo simulations combined with a Bayesian inference technique to obtain dynamics and are consistent with predictions from spin-wave theory.

Figure 1

Instantaneous correlation function $D^{\alpha }\left(\vec{q},0\right)$ vs $\vec{q}$ along the path in the Brillouin zone indicated in the upper left corner of (a). The different curves are for different values of the magnetic field $B$ specified in the legends. (a) is for longitudinal spin polarizations $\left(\alpha =z\right)$ while the (b) is for transverse polarizations $\left(\alpha =x\right)$. The error bars are smaller than the symbol size.

Figure 2

Gray-scale plot of $S^z\left(Q,\omega \right)$ where $q$ takes values along a path in the Brillouin zone specified in the inset. The thin white curve indicates the renormalized linear spin-wave dispersion, $Z_c{\omega }_s\left(\vec{q}\right)$.

Figure 3

Gray-scale plot of $S^z\left(\vec{q},\omega \right)$ along the $\vec{q}$ path indicated in Fig. 1. The thin white curve is the perturbative result for the spin-wave dispersion using the self-energy.

Figure 4

Gray-scale plot of $S^z\left(\vec{q},\omega \right)$ along the $\vec{q}$ path indicated in Fig. 1 for $B/J=3.5$. The thin black curve is the magnon linewidth $\Gamma$ calculated using the golden rule in Eq. (8).

Figure 5

Line shapes of the dynamic structure factor at $\left(\pi /2,\pi /2\right)$ for three different values of magnetic field as indicated in the legend. Here the system size is $L=16$ and the inverse temperature is $\beta J=200$.