Calculation of Linear and Nonlinear Optical Responses Based on Kadanoff-Baym and Tight-Binding Approaches

Understanding light–matter interaction in correlated materials requires theoretical frameworks that go beyond equilibrium and linear-response approximations. In this work, we present a unified approach for calculating linear and nonlinear optical responses based on the Kadanoff–Baym equations (KBE) combined with an atomistic tight-binding (TB) representation of the electronic structure. The KBE provide a rigorous real-time formulation of quantum dynamics, explicitly incorporating memory effects and many-body correlations through self-energies. Using this formalism, we simulate time-dependent charge density, current, and polarization, from which both linear susceptibilities and nonlinear optical coefficients are obtained.

The tight-binding framework enables efficient representation of complex materials, including layered and low-dimensional systems, while retaining orbital character and gauge-consistent coupling to external fields. We compare the full two-time KBE formulation with the generalized Kadanoff–Baym ansatz (GKBA), which reconstructs two-time Green’s functions from single-time quantities, significantly reducing computational cost while preserving dynamical correlations.

Our results provide a pathway toward first-principles, time-resolved modeling of ultrafast optical phenomena in strongly correlated materials. In this talk we will demonstrate the ab-initio calculations of the linear and nonlinear optical properties of 2D materials, including MoS₂, GaSe, and Nb₃Cl₈, and compare our results with GW-BSE and TD-BSE results from Yambo.