Speaker
Description
Quantum integrability is rooted in Bethe ansatz, which is a powerful mathematical framework that has been very successful in obtaining exact solutions to many-body Hamiltonians. Bethe ansatz in both the coordinate and algebraic incarnations is only applicable to Hamiltonians with constant coupling strengths. In this talk I will introduce the recently developed generalized Bethe ansatz framework, an exact method for solving a broad class of strongly interacting models with time-dependent coupling strengths that are based on quantum Yang-Baxter algebra. In this framework, the problem of solving the time-dependent Schrodinger equation can be reduced to a set of matrix difference equations, namely quantum Knizhnik-Zamolodchikov (qKZ) equations. The consistency of the solution gives rise to a set of constraint conditions on the time-dependent coupling strengths. For coupling strengths satisfying these conditions, the system is integrable, and the solution to the qKZ equations provides the explicit form of the exact wavefunction. I will further demonstrate that the conditions imposed by integrability are exactly equivalent to the renormalization-group flow equations of the corresponding Hamiltonian with time-independent coupling strengths, when the physical time of the driven system is identified with the logarithmic cutoff scale of the static problem t = log Λ, thereby revealing a deep connection between time-dependent integrability and the renormalization group flow. I will demonstrate how this formalism yields closed-form, non-perturbative solutions to paradigmatic models based on quantum Yang-Baxter algebra such as the Kondo model, the SU(2) Gross-Neveu model etc., whose interaction strengths vary in time. If time permits, I will conclude by discussing how this method can be applied to analyze novel dynamical phases that arise in driven quantum systems.