Direct evidence of the BOW and TS states in the half-filled one-dimensional extended Hubbard model

•We get the quantum phase diagram of the half-filled one-dimensional EHM from the quantum information point of view.•The BOW state and its boundary condition is confirmed by the entanglement entropy.•Direct evidences of the phase transitions of TS-SS and TS-SDW are shown.

Taking periodic boundary condition into account, we study the quantum phase diagram of the half-filled one-dimensional extended Hubbard model using the density matrix renormalization group (DMRG) approach. The entanglement entropy clarifies the controversy about the existence of the bond-order-wave state, and the crossover from the first order to continuous phase transition along the phase transition line between the charge-density-wave and bound-order phases is clearly demonstrated. Meanwhile, we show the direct evidences of the phase transition from the singlet to triplet superconducting phases as well as the triplet superconducting to the spin-density-wave phase transition from the entanglement point of view.