Role of correlated hopping is studied using extended Falicov–Kimball model in a small cluster. A discontinuous insulator-to-metal transition is observed at a critical 𝑓-level energy. Transition is sharper for larger correlated hopping. In the specific heat curves a two-peak structure consisting of a sharp peak followed by a Schottky-type broad peak is exhibited. In a limited parameter region, some heavy-fermion like characteristics have been observed

The two-dimensional (2D) extended Falicov–Kimball model has been studied to observe the role of nonlocal Coulomb interaction ($U_{\text{nc}}$) using an exact diagonalization technique. The f-state occupation ($n^f$), the f–d intersite correlation function ($c_{\text{fd}}$), the specific heat (𝐶), entropy (𝑆) and the specific heat coefficient (𝛾) have been examined. Nonlocal Coulomb interaction-induced discontinuous insulator-to-metal transition occurs at a critical f-level energy. More ordered state is obtained with the increase of $U_{\text{nc}}$. In the specific heat curves, two-peak structure as well as a singlepeak structure appears. At low-temperature region, a sharp rise in the specific heat coefficient 𝛾 is observed. The peak value of 𝛾 shifts to the higher temperature region with $U_{\text{nc}}$.