Extended one-dimensional Hubbard model: A small-cluster approach

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Abstract
The one-dimensional Hubbard model with nearest-neighbor hopping, first- and second-nearest-neighbor particle interactions, and one particle per site is reexamined by means of a small-crystal approach—an exact solution of a four-site cluster with periodic boundary conditions. Lines of symmetry crossing as well as singular lines and points are found. Analysis of correlation functions indicates that although there are smooth, strong changes as the parameters approach the values of the charge-to-spin-density-wave transition (a suggestion of an incipient second-order transition), the actual change involves a crossover between unrelated symmetries (a clear indication of a first-order transition). The relatively simple calculation and its results agree well with previous Monte Carlo numerical simulations and settles the unresolved question of the order of the density-wave transition.