Cluster perturbation theory for the Hubbard model: the pinning of chemical potential

In this paper we study the single-band two-dimensional Hubbard model in the framework of the cluster perturbation theory. Consideration is limited to nearest-neighbor approximation. The original two-dimensional square lattice is divided into clusters of $2\times2$, forming a square superlattice. The complete set of eigenvectors and eigenvalues of a single cluster is determined by exact diagonalization method. On this basis, we construct X-operators, through which overrides the Hamiltonian of the problem. The spectral function is computed within the Hubbard-I approximation. This function allows to explore the distribution of spectral weight of the quasiparticles in the Hubbard subbands. The effect of the in-gap states at the pinning of the chemical potential at low concentrations of holes is explored.