发表机构
Condensed Matter Theory Center, Department of Physics, University of Maryland; Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（马里兰大学凝聚态理论中心物理系; 加州大学洛杉矶分校曼尼·L·巴乌米克理论物理研究所物理与天文学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明各向异性电流-电流微扰SU(2)_1 WZW模型的RG极限环等价于其相互作用强度的周期性实时演化，通过可积Bethe ansatz建立了RG流与量子动力学间的精确对应。
AI 中文摘要
我们建立了各向异性电流-电流微扰$SU(2)_1$ Wess-Zumino-Witten (WZW)模型中重整化群(RG)演化与实时量子动力学之间的精确对应关系。利用其可积费米子表示，我们通过广义Bethe ansatz构造了精确的时间依赖多体波函数，并证明周期性边界条件导致与XXZ三角$R$-矩阵相关的量子Knizhnik-Zamolodchikov方程，该矩阵对应于在其自旋-$1/2$求值表示中求值的量子仿射代数$\mathcal{U}_q(\widehat{\mathfrak{sl}_2})$。这些方程的一致性约束了纵向和横向相互作用强度的时间演化。在普适区间，当物理时间与对数RG尺度等同后，这些可积性条件精确等价于Berezinskii-Kosterlitz-Thouless RG流方程。因此，各向异性电流-电流微扰$SU(2)_1$ WZW模型的RG极限环被实现为其相互作用强度的周期性实时演化。我们的结果为RG极限环提供了精确的动力学实现，并在循环RG流、量子可积性和周期驱动相互作用量子场论之间建立了直接联系。
英文摘要
We establish an exact correspondence between renormalization-group (RG) evolution and real-time quantum dynamics in the anisotropic current-current perturbed $SU(2)_1$ Wess-Zumino-Witten (WZW) model. Using its integrable fermionic representation, we construct the exact time-dependent many-body wavefunction by means of the generalized Bethe ansatz and show that periodic boundary conditions lead to quantum Knizhnik-Zamolodchikov equations associated with the XXZ trigonometric $R$-matrix, which corresponds to the quantum affine algebra $\mathcal{U}_q(\widehat{\mathfrak{sl}_2})$ evaluated in its spin-$1/2$ evaluation representation. Consistency of these equations constrains the temporal evolution of the longitudinal and transverse interaction strengths. In the universal regime, these integrability conditions are exactly equivalent to the Berezinskii-Kosterlitz-Thouless RG flow equations upon identifying physical time with the logarithmic RG scale. Consequently, the RG limit cycles of the anisotropic current-current perturbed $SU(2)_1$ WZW model are realized as periodic real-time evolution of its interaction strengths. Our results provide an exact dynamical realization of RG limit cycles and establish a direct connection between cyclic RG flows, quantum integrability, and periodically driven interacting quantum field theories.
