Higher-Order Susceptibilities in Extended Kitaev Models Computed Via Krylov-Space Based Methods

Recently, it was proposed that techniques measuring higher-order response, such as two-dimensional coherent spectroscopy (2DCS), could provide more distinguishable signatures for states and excitations potentially causing continua in linear response. The numerical calculation of nonlinear response functions can, however, be computationally very demanding. Here we propose an efficient Lanczos-based method that computes higher-order susceptibilities such as χ₂(ω_t,ω_τ) and χ₃(ω_t,ω_τ) directly in the frequency domain, avoiding explicit numerical time evolutions. As an application case, we consider extended Kitaev models, that are relevant to α-RuCl₃ and related materials. This way, we compare the signatures of excitations of magnetically ordered, spin-liquid, and field-induced phases with one another.