Dynamical Nonlinear Optic Coefficients from the Symmetrized Density Matrix Renormalization Group Method

TL;DR

This paper extends the SDMRG method to calculate dynamic nonlinear optical coefficients in long fermionic chains, providing new insights into their excitation properties and behavior.

Contribution

It introduces the first DMRG-based approach to compute the dynamics of fermionic systems' nonlinear optical responses.

Findings

Computed dynamic polarizabilities and third-order polarizabilities for Hubbard and $U-V$ chains.

Analyzed the relationship between optical responses and low-lying excitation gaps.

Demonstrated the method's effectiveness in long-chain fermionic systems.

Abstract

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, $\alpha_{ij}(\omega)$, and third-order polarizabilities $\gamma_{ijkl}(\omega,\omega,\omega)$ of the Hubbard and "$U-V$" chains in an $all-trans$ polyacetylene geometry, with and without dimerization. We rationalize the behavior of $\bar{\alpha}$ and $\bar{\gamma}$ 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.