Low-lying excited correlated electronic states of cycloparaphenylene and cyclacene: An efficient symmetrized density matrix renormalization group study with periodic boundary condition

One-dimensional and quasi-one-dimensional correlated fermionic models can be studied efficiently using the Density Matrix Renormalization Group (DMRG) method with open boundary conditions. Although the implementation of the conventional DMRG technique in investigating a fermionic model with a periodic boundary condition (PBC) is still challenging due to the demand of high computational facility, this work reports the efficient use of the symmetrized DMRG (SDMRG) technique in studying the low-lying correlated excited-states of radially π-conjugated cycloparaphenylene ([6]CPP) and [n]cyclacene molecules within the Pariser-Parr-Pople (PPP) model Hamiltonian with adequate computational cost. The low-lying correlated singlet excited energies of [6]CPP calculated within the PPP model are in very good agreement with experiment. Compared to [6]CPP, the numerical accuracy of DMRG calculations for highly correlated [n]cyclacene depends on the number of DMEV basis (m). Such a study shows an efficient pathway to implement the SDMRG technique in studying fermionic systems with PBC in the future.