Parametric pumping of the two-dimensional quantum spin liquid

With the help of the exact solution of the Kitaev model the parametric pumping of the two-dimensional quantum spin liquid under the action of the ac magnetic field is studied. In the dynamical regime the field produces oscillations of the magnetization with the field's frequency, modulated by the Rabi-like oscillations. In the steady-state regime, the Rabi-like oscillations are damped. The absorption of the ac field by the Kitaev spin model is finite and manifests resonance features. Such a behavior is generic for quantum spin liquids with fermionic excitations, and it is different from the linear spin-wave response of magnetically ordered systems to such a parametric pumping.

Figure 1

The contribution of band excitations to the normalized absorption of the ac magnetic field by the Kitaev honeycomb spin-1/2 model (the gapless case $|J_x-J_y|\le J_z\le J_x+J_y$) as a function of the frequency $\omega$ of the ac field and the coupling $J_z$. We used the parameters $J_x=1,J_y=0.5$.

Figure 2

The frequency dependence of the absorbed power of parametric pumping by band states of the Kitaev honeycomb model for the gapped case with the coupling $J_z>J_x+J_y$ with the parameters $J_x=1,J_y=0.5$, and $J_z=2$.

Figure 3

The frequency dependence of the normalized absorbed power of the parametric pumping by the band states of the Kitaev honeycomb model for the case $J_x=J_y=1$ and $J_z=0.5$ (gapless excitations).