Geodesic
Cluster perturbation theory for the Hubbard model: the pinning of chemical potential
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 2, pp. 162-167.

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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.
Keywords: cluster perturbation theory, Hubbard model, strong electron correlation, exact diagonalization, X-operators, density of states. 
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Sergey V. Nikolaev; Sergey G. Ovchinnikov. Cluster perturbation theory for the Hubbard model: the pinning of chemical potential. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 2, pp. 162-167. http://geodesic.mathdoc.fr/item/JSFU_2011_4_2_a2/

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