In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.

中文翻译：

---

具有普遍变形的哈密顿量的Floquet共形场理论

在这项工作中，我们研究了1 + 1D的Floquet共形场理论（CFT）中的非平衡动力学，其中驱动哈密顿量涉及由任意光滑函数空间调制的能量动量密度。这概括了早期的工作，这些工作仅限于Floquet哈密顿量的正弦平方变形类型，在$ \ mathfrak {sl} _2 $子代数内运行。在这里，我们显着地表明，在这种基于几何方法的，涉及整个Virasoro代数的广义情况下，问题仍然可以解决。发现相图是由算子演化的频闪轨迹确定的。在操作员进化过程中是否存在空间固定点表明，驱动的CFT处于加热/非加热阶段，在该阶段纠缠熵随时间增长/振荡。此外，加热方式可进一步细分为多个阶段，具有不同的纠缠模式和能量动量密度的空间分布，其特征在于空间固定点的数量。这些不同加热相之间的相变可以简单地通过改变驱动哈密顿量的施加持续时间来实现。我们用具体的CFT示例演示了一般特征，并将结果与​​晶格计算进行比较，并找到了惊人的一致性。这些不同加热相之间的相变可以简单地通过改变驱动哈密顿量的施加持续时间来实现。我们用具体的CFT示例演示了一般特征，并将结果与​​晶格计算进行比较，并找到了惊人的一致性。这些不同加热相之间的相变可以简单地通过改变驱动哈密顿量的施加持续时间来实现。我们用具体的CFT示例演示了一般特征，并将结果与​​晶格计算进行比较，并找到了惊人的一致性。