AI 中文总结
研究二维横向场伊辛模型实时量子动力学，用模糊球正则化方案，通过线性斜坡横向场研究相关量有限时间标度行为，确定不同猝灭率下的标度规律，为强耦合 CFT 实时临界动力学研究提供途径。
AI 中文摘要
我们使用最近开发的模糊球正则化方案重新审视二维横向场伊辛模型的实时量子动力学问题。通过将横向场从顺磁相线性斜坡到临界状态，我们研究了平方序参量\(\langle m_z^2 \rangle\)、激发能密度\(Q\)以及\(m_z\)的两点关联函数的有限时间标度行为。我们通过数值方法确定，在中等猝灭率下，\(\langle m_z^2 \rangle\)遵循由三维伊辛普适类临界指数设定的传统基布尔 - 祖雷克预测，关联函数呈现预期的指数衰减，其关联长度可用于估计冻结时间/长度中的非普适标度系数。相比之下由于能谱中对称性强制的能级稀疏导致的大有效有限尺寸间隙，激发能密度\(Q\)在可用系统尺寸下未达到相同的标度区域。在慢猝灭率下，\(\langle m_z^2 \rangle\)和\(Q\)的通用准绝热标度得以恢复。由于模糊球构造不仅可以实现伊辛共形场论（CFT），还可以实现广泛的\((2 + 1)d\) CFT 家族，我们的结果为强耦合 CFT 的实时临界动力学建立了一条途径，否则这些动力学在计算上具有挑战性。
英文摘要
We revisit the problem of \textit{real-time} quantum dynamics of the paradigmatic two dimensional transverse-field Ising model using the recently developed fuzzy sphere regularization scheme. By linearly ramping the transverse field from the paramagnetic phase to criticality, we study the finite-time scaling behavior of the squared order parameter $\langle m_z^2 \rangle$, the excitation energy density $Q$, and the two-point correlation function of $m_z$. We establish numerically that, at intermediate quench rate, $\langle m_z^2 \rangle$ follows the conventional Kibble-Zurek prediction set by the critical exponents of the $3$D Ising universality class, and the correlation function exhibits the expected exponential decay whose correlation length can be used to estimate the non-universal scaling coefficient in the freeze-out time/length. In contrast, the excitation energy density $Q$ does not reach the same scaling regime at available system sizes due to large effective finite-size gap from symmetry-enforced level sparsity in the energy spectrum. At slow quench rates the universal quasi-adiabatic scaling for both $\langle m_z^2 \rangle$ and $Q$ is recovered. Since the fuzzy sphere construction can realize not only the Ising conformal field theory (CFT), but a broad family of $(2+1)d$ CFTs, our results establish a route to the real-time critical dynamics of strongly coupled CFTs that are otherwise computationally challenging to study.
Comments4.5 pages with 4 figures in main text + 1.5 pages of appendix
