A comprehensive description of notable phenomena of low-dimensional periodic systems, such as the photoexcitation and Dirac point, requires the multiconfigurational electronic structure method beyond the $\mathrm{\Gamma }$-point approximation. Here, we introduce an ab initio framework we call PBC-DMRGCI by achieving the support of complex-valued wave functions; this framework integrates the complete active space configuration interaction (CASCI) approach with periodic boundary conditions (PBC) and the density matrix renormalization group (DMRG) solver. Combined with the supercell method, the PBC-DMRGCI framework enables the accurate treatment of strong electron correlation within the active spaces at any single $\mathbf{k}$ point in the first Brillouin zone. Taking the one-dimensional ${\mathrm{H}}_2$ chain, one-dimensional trans-polyacetylene, and the two-dimensional $\mathrm{Mo}{\mathrm{S}}_2$ supercell as prototypical systems, the PBC-DMRGCI method demonstrates its power in revealing complex many-body effects on both the ground state and excited states. Moreover, by operating at any single $\mathbf{k}$ point in the first Brillouin zone, the PBC-DMRGCI framework facilitates the exploration of electron correlation beyond the $\mathrm{\Gamma }$-point approximation, thereby opening avenues for the study of momentum-resolved excitations in strongly correlated solids.

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• Electronic structure
• Excitons
• Photoinduced effect
• Density functional theory development
• Density matrix renormalization group