AI 中文总结
研究$4\times4$环面上手性$J_1$-$J_2$-$K$海森堡模型的弗洛凯动力学，通过计算单周期传播子等方法，发现拓扑双重态在特定条件下具有频闪稳定性，为热力学极限下预热弗洛凯CSL的研究提供了依据。
AI 中文摘要
我们研究了$4\times4$环面上手性$J_1$-$J_2$-$K$海森堡模型的两步弗洛凯动力学，交替其非手性海森堡部分$H_{\rm AF}$和手性面元部分$H_K$，在静态模型（在无限频率极限下恢复）具有准简并、谱孤立的手性自旋液体（CSL）拓扑双重态的参数点。精确计算了所有动量/旋转对称扇区的单周期传播子。结果表明，降低频率时，拓扑双重态在驱动下能在远高于折叠态首次在准能量中穿过它的频率$\omega_{\mathrm{res}}\simeq 11.5 J_1$时存活：弗洛凯本征态的时间平均能量对折叠的弗洛凯谱进行排序，表明双重态在$\omega\simeq6J_1$以下仍为谱的孤立底部，而数千个周期的频闪时间演化表明，对于$\omega\gtrsim \omega_{\mathrm{res}}$没有加热，低于此频率只有缓慢吸收。在折叠区域出现的准能量共振在平均能量中不可见，将它们识别为参数性弱避免交叉。我们认为，这种由局部能量尺度而非广泛的多体带宽控制稳定性的机制，正是预期在热力学极限中存活下来的机制，其中预热的弗洛凯CSL应在由局部尺度设定的阈值以上的$\omega$中持续存在，加热时间在$\omega/J_1$中呈指数增长。一致地，静态问题的最优$D = 3$手性PEPS仍然可以描述折叠区域深处的驱动双重态，局部张量基本不变。
英文摘要
We study the two-step Floquet dynamics of the chiral $J_1$-$J_2$-$K$ Heisenberg model on the $4\times4$ torus, alternating its non-chiral Heisenberg part $H_{AF}$ and its chiral plaquette part $H_K$, at a parameter point where the static model hosts a quasi-degenerate, spectrally isolated chiral-spin-liquid (CSL) topological doublet. The one-period propagator is computed exactly in all symmetry sectors. Decreasing the frequency, the doublet survives the drive far beyond the frequency $ω_{res}\simeq 11.5 J_1$ at which folded states first cross it in quasienergy: the time-averaged energy of the Floquet eigenstates, which orders the folded spectrum, shows that the doublet remains the isolated bottom of the spectrum down to $ω\simeq 6J_1$, while stroboscopic time evolution over thousands of periods shows no heating for $ω\gtrsimω_{res}$ and only slow absorption below. The quasienergy resonances of the folded regime are invisible in the average energy, identifying them as parametrically weak avoided crossings. We argue that this mechanism, stability controlled by local energy scales rather than by the extensive many-body bandwidth, is of the type expected to survive in the thermodynamic limit, where a prethermal Floquet CSL should persist for $ω$ above a threshold set by local scales, with heating times exponentially long in $ω/J_1$, a conjecture that larger clusters can now test. Consistently, the optimal $D=3$ chiral PEPS of the static problem still describes the driven doublet deep in the folded regime, with an essentially unchanged local tensor. Finally, we show that the drive is realizable on existing quantum simulators, via an explicit digital pulse sequence of XY-type two-spin gates on the four bond colours of the square lattice, with an infidelity of $1.5\times10^{-5}$ per period.
CommentsRevised version; responds to referee report. 27 pages, 11 figures
