The Holstein t-J model extended by the nearest-neighbor (NN) hole-phonon (h − ph) interaction ( \(\lambda _2\) ) and inter-site Coulomb repulsion (V/t) is studied using the exact diagonalization method in the context of high-temperature superconducting cuprates. The exotic physics, characteristics, and stability of polarons and bipolarons are explored. Polarons, large hole bipolarons (LHBP), and Small Hole Bipolarons (SHBP) exist in the Holstein t-J model, depending on the relative strength of the h − ph interaction and inter-site Coulomb repulsion. The role of V/t is to suppress the formation of these hole bipolarons. The transition region from polarons to different types of bipolarons’ is shifted to higher magnitudes of \(\lambda _2\) with the increasing strength of intersite Coulomb repulsion. Moreover, increased phonon energy generally induces the formation of bipolarons. A schematic phase diagram is presented. A single peak in specific heat is observed in the accessible temperature range rising due to charge fluctuations. At low temperatures, the system becomes more ordered above the critical value of \(\lambda _2\) in the anti-adiabatic limit.
