Superconducting correlations in the one-dimensionalt-Jmodel

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Abstract
The t-J model is the simplest Hamiltonian for strongly correlated electrons, in which a superconducting phase may be present. This paper discusses superconducting correlation functions of the one-dimensional t-J model obtained from exact diagonalization of finite systems. Singlet and triplet channels are examined and compared with each other; the results are interpreted in terms of the Luttinger-liquid theory. A detailed study is made of the small-J limit, where the special form of the ground-state wave function allows a thorough study of correlation functions, including logarithmic corrections to the leading power-law decay. In addition, the effect of a magnetic field is also examined, since singlet and triplet superconducting correlations are competitive at zero field. It turns out that the magnetic field modifies the superconducting correlations in an interesting way. In particular, an analog of the Fulde-Ferrell state is found for some intermediate J.