标题： 量子基尼兹尼克-扎莫洛德奇科夫方程与时间依赖相互作用强度的量子场论的可积性 显示英文标题

标题： Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-dependent Interaction Strength

摘要： 在本文中，我们考虑解决具有时间依赖相互作用强度的量子场论问题。 我们表明，最近提出的框架[P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)]，这是常规Bethe假设技术的推广，提供了精确的多体波函数。 在此框架中，时间依赖的薛定谔方程被简化为一组解析差分方程和矩阵差分方程，称为量子Knizhnik-Zamolodchikov（qKZ）方程。 解的一致性导致对时间依赖相互作用强度的约束。 对于满足这些约束的相互作用强度，系统是可积的，qKZ方程和解析差分方程的解提供了满足时间依赖薛定谔方程的多体波函数的显式形式。 我们通过考虑具有时间依赖相互作用强度的$SU(2)$Gross-Neveu模型提供了一个具体例子。 使用此框架，我们解决了具有最一般时间依赖相互作用强度的模型，并得到了波函数的显式形式。 显示英文摘要

摘要： In this paper we consider the problem of solving quantum field theories with time dependent interaction strengths. We show that the recently formulated framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], which is a generalization of the regular Bethe ansatz technique, provides the exact many-body wavefunction. In this framework, the time-dependent Schrodinger equation is reduced to a set of analytic difference equations and matrix difference equations, called the quantum Knizhnik-Zamolodchikov (qKZ) equations. The consistency of the solution gives rise to constraints on the time-dependent interaction strengths. For interaction strengths satisfying these constraints, the system is integrable, and the solution to the qKZ and the analytic difference equations provides the explicit form of the many-body wavefunction that satisfies the time-dependent Schrodinger equation. We provide a concrete example by considering the $SU(2)$ Gross-Neveu model with time dependent interaction strength. Using this framework we solve the model with the most general time-dependent interaction strength and obtain the explicit form of the wave function.