Staggered field induced dynamical effects in a quantum spin chain

The response of the one-dimensional antiferromagnetic spin-1/2 chain to the ac staggered magnetic field is studied within the Hartree-Fock-like approximation. For a closed system that field produces oscillations of the magnetization with the frequency of the ac field, modulated by the large number of small Rabi frequencies. In the open system the Rabi oscillations decay due to relaxation processes. It is shown that those oscillations also contribute to the dynamics of the entanglement of the system. The calculated temperature and frequency dependence of the dynamical characteristics is strictly nonmonotonic, reflecting the complicated character of the common action of the homogeneous and staggered dc field.

Figure 1

The time dependence of the magnetization of the spin chain per site in the dynamical regime with ${\mu }_1=1.1,{\mu }_2=0.9,J_1=1.2,J_2=0.8,J_{1z}=J_{2z}=0$ at $H=0$ and the temperature $T=0.1$ as a response to the ac magnetic field with $h=0.1$ and $\omega =1$ for $\gamma =0$.

Figure 2

The same as in Fig. 1 but for $\gamma =0.01$.

Figure 3

The time dependence of the magnetization of the spin chain per site in the steady-state regime. The parameters are the same as in Figs. 1 and 2 (for $\gamma =0.01$). (Only short times are shown, however similar oscillations persist for much longer times.)

Figure 4

The frequency dependence of the dynamical magnetic staggered susceptibility of the spin chain per site in the linear in $h$ regime. We used the parameters ${\mu }_1=1.1,{\mu }_2=0.9$, and $J_{1z}=J_{2z}=0$ for $H=0$ and low-temperature $T=0.001$ at $\gamma =0.1$. For the dimerized chain $J_1=1.2,J_2=0.8$ the black dotted line shows the behavior of ${\chi }^{\prime }$; the green solid line shows ${\chi }^{″}$. For the homogeneous chain $J_1=J_2=1$ the blue long-dashed line shows the behavior of ${\chi }^{\prime }$; the red dashed line shows ${\chi }^{″}$.

Figure 5

The frequency dependence of the dynamical magnetic staggered susceptibility of the spin dimer in the linear-in-$h$-response regime. We used the parameters ${\mu }_1=1.1,{\mu }_2=0.9$, and $J_2=J_{1z}=J_{2z}=0$ for $H=0$ and low-temperature $T=0.001$ at $\gamma =0.1$. The black solid line shows ${\chi }_{\dim }^{\prime }$, whereas the dashed red line is ${\chi }_{\dim }^{″}$.

Figure 6

The frequency and magnetic-field dependence of the absorbed power of the ac field by the spin chain per site (divided by $h^2$) in the linear-response regime for $J_{1z}=J_{2z}=0,J_1=1.2,J_2=0.8,{\mu }_1=1.1,{\mu }_2=0.9$, and $T=0.1$.

Figure 7

The temperature and magnetic-field dependence of the absorbed power of the ac field by the spin chain per site (divided by $h^2$) in the linear-response regime for $J_{1z}=J_{2z}=0,J_1=1.2,J_2=0.8,{\mu }_1=1.1,{\mu }_2=0.9$, and $\omega =1.9$.

Figure 8

The frequency and magnetic-field dependence of the absorbed power of the ac field by the dimer (divided by $h^2$) for $J_{1z}=J_{2z}=J_2=0,J_1=1,{\mu }_1=1.1,{\mu }_2=0.9,h=0.1$, and $T=0.1$.

Figure 9

The time dependence of the addition to the tangle of the spin chain in the closed case. The parameters are the same as in Fig. 1 but for $T=0$.

Figure 10

The time dependence of the addition to the concurrence of the spin chain in the open case. The parameters are the same as in Fig. 1 but for $T=0.1,\gamma =0.01$, and $h=0.015$.