Dynamic destruction of magnetic order in a quantum Ising chain with oscillating transverse field

TL;DR

This work analyzes the driven quantum Ising chain in its low-energy domain-wall sector under a periodic transverse field. By projecting onto single-domain-wall states, the authors derive an effective two-subspace Hamiltonian, and in the relevant subspace obtain a time-dependent 1D hopping model with a linear tilt, leading to an instantaneous Stark ladder with equally spaced levels $E_m = m\omega_0$ and spacing $\omega_0 = 2B_z$. The dynamics exhibit Bloch oscillations off resonance, preserving magnetic order, while at resonance $\omega = \omega_0$ the domain wall spreads and magnetic order is destroyed, as shown by analytical solutions in the Floquet framework and corroborated by numerical simulations of fidelity $F(t)$, magnetization $M(t)$, and entanglement entropy $S(t)$ for single and double domain-wall configurations. This reveals a narrow resonant window where a monochromatic field nontrivially controls quantum spin dynamics, with potential applications in quantum-device engineering. Key results include the separation into decoupled subspaces, the instantaneous Stark ladder with spacing $\omega_0$, and the resonance-induced transition from localized, order-preserving dynamics to dispersive, disorder-inducing dynamics.

Abstract

We study the dynamic response of magnetic domain walls in low-lying excited states of an Ising chain to an oscillating transverse field. Based on the exact instantaneous eigenstates, we find that when the frequency of the external field is in off-resonant regions, the domain wall exhibits Bloch oscillation, maintaining the magnetic order. However, the magnetic order is destroyed when the field is at resonant frequency. Numerical simulations of the dynamics of magnetization and entanglement entropy for initial states with single and double domain walls accord with the predictions. These findings reveal the nontrivial effect of a monochromatic electromagnetic field on quantum spin dynamics.

Figures (3)

• Figure 1: Schematic illustrations of the system we studied and the main results of this work. (a) A quantum chain with nearest-neighbor Ising-type interaction of strength $J$. There are two external fields: one is a constant field in the $z$-direction, while the other is a periodic field with frequency $\omega$ in the $x$-direction. The configuration of spins represents an initial state for the following dynamic processes. This initial state is a ferromagnetic state with a single domain wall at the center. The main results of this paper are sketched in the following. (b) In the case of decoupling, that is, when $J=0$, every spin in the same domain evolves in the same phase, leaving the domain wall unchanged. (c) When the driving field is off-resonance, the domain wall is slightly disturbed, leaving it almost unchanged. (d) When the driving field is on-resonance, the domain wall is destroyed, resulting in a disordered phase.
• Figure 2: Plots of $F(t)$, $M(t)$, and $S(t)$, defined in Eqs. (\ref{['F(t)']}), (\ref{['M(t)']}) and (\ref{['S(t)']}), respectively, for the evolved state in Eq. (\ref{['onewall']}), obtained by numerical solution of the Schrödinger equation via the fourth-order Runge-Kutta method for a finite-size chain with several typical values of frequency $\mathcal{\omega}$. Here, $T_{0}=\pi/B_{z}$ is the resonance period. (b1), (b2), and (b3) are the corresponding plots of $m_{j}(t)$, given in Eqs. (\ref{['m_j(t)']} ), corresponding to three typical values of frequency $\omega=0.2$, $\omega=0.35$ and $\omega=0.4$, respectively. The other parameters are $J=1, g=0.05, B_{z}=0.2$ and $N=20$. We can see that the patterns in (b1), (b2), and (b3) clearly reflect the impact of the oscillating field and provide an intuitive picture for understanding the curves in (a1), (a2), and (a3). The results are in accordance with our predictions.
• Figure 3: The same plots as those in Fig. \ref{['fig2']}, obtained with the same parameters but for the initial state with double domain walls given in Eq. (\ref{['twowalls']}), are consistent with our predictions.