边界量子Knizhnik-Zamolodchikov方程与含时体和边界耦合强度的量子场论的可积性
Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths
- Condensed Matter Theory Center, Department of Physics, University of Maryland（马里兰大学物理系凝聚态理论中心）
- Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理与天文学系马尼·L·巴乌米克理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究将广义Bethe ansatz框架扩展到含时体与边界耦合的开放边界条件情形，推导得到边界量子Knizhnik-Zamolodchikov方程，证明静态模型RG不变量对应含时模型动力学不变量，为相关量子场论可积性研究提供了新方法。
AI中文摘要：
文献[P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)]中提出的广义Bethe ansatz框架为求解含时耦合强度、具有周期性边界条件的量子多体系统提供了统一框架。本研究将该框架扩展到开放边界条件情形，此时除了体相互作用随时间变化外，边界条件也显式随时间变化。我们证明，对于可积的含时体耦合强度，广义Bethe ansatz框架提供了与可积性兼容的含时边界条件，并将含时薛定谔方程约化为一组称为边界量子Knizhnik-Zamolodchikov（BqKZ）方程的矩阵差分方程。BqKZ方程的解给出了精确波函数的显式形式。我们进一步证明，对应静态模型的RG不变量与含时模型中的动力学不变量一致。
英文摘要：
The generalized Bethe ansatz framework formulated in [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)] provides a unified framework to find exact solutions to quantum many-body systems with time-dependent coupling strengths with periodic boundary conditions. In this work we extend this framework to the case of open boundary conditions where in addition to the time-dependent interactions in the bulk, the boundary conditions are explicitly time-dependent. We show that for integrable time-dependent bulk coupling strengths, the generalized Bethe ansatz framework provides the time-dependent boundary conditions compatible with integrability and reduces the time-dependent Schrodinger equation to a set of matrix difference equations called the boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations. The solution to the BqKZ equations provides the explicit form of the exact wavefunction. We further show that the RG invariants of the corresponding static model identify with the dynamical invariants in the time-dependent model.
