We extend the symmetrized density matrix renormalization group (SDMRG) method to compute the dynamic nonlinear optic coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace we obtain the dynamic polarizabilities,
αij(ω), and third-order polarizabilities
γijkl(ω,ω,ω) of the Hubbard and "
U−V" chains in an
all−trans polyacetylene geometry, with and without dimerization. We rationalize the behavior of
αˉ and
γˉ on the basis of the low-lying excitation gaps in the system. This is the first study of the dynamics of a fermionic system within the DMRG framework.
Abstract We investigate measures of non-Markovianity in open quantum systems governed by Gaussian free fermionic dynamics. Standard indicators of non-Markovian behavior, such as the BLP and LFS measures, are revisited in this context. We show that for Gaussian states, trace-based distances—specifically the Hilbert–Schmidt norm—and second-order Rényi mutual information can be efficiently expressed in terms of two-point correlation functions, enabling practical computation even in systems where the full-density matrix is intractable. Crucially, this framework remains valid even when the density matrix of the system is an average over stochastic Gaussian trajectories, yielding a non-Gaussian state. We present efficient numerical protocols based on this structure and demonstrate their feasibility through a small-scale simulation. Our approach opens a scalable path to quantifying non-Markovianity in interacting or measured fermionic systems, with applications in quantum information and non-equilibrium quantum dynamics. Graphic Abstract