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 wave function. 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 wave function that satisfies the time-dependent Schrodinger equation. We provide a concrete example by considering the $SU\left(2\right)$ 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.

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• Spin-singlet pairing
• Superconducting order parameter
• Topological superconductors
• Bethe ansatz
• Conformal field theory
• Duality
• Exact solutions for many-body systems
• Field & string theory models & techniques
• Gross-Neveu model
• Hubbard model
• Second quantization
• Su-Schrieffer-Heeger model