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Register a new userPairing Glue in the Hubbard and t-J Models
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The question of whether one should speak of a pairing glue in the Hubbard and t-J models is basically a question about the dynamics of the pairing interaction. If the dynamics of the pairing interaction arises from virtual states, whose energies correspond to the Mott gap, and give rise to the exchange coupling J, the interaction is instantaneous on the relative time scales of interest. In this case, while one might speak of an instantaneous glue, this interaction differs from the traditional picture of a retarded pairing interaction. However, if the energies correspond to the spectrum seen in the dynamic spin susceptibility, then the interaction is retarded and one speaks of a spin-fluctuation glue which mediates the d-wave pairing. Here we present results from numerical studies which provide insight into this question.
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A dynamic cluster quantum Monte Carlo algorithm is used to study a spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model with an on-site Coulomb interaction equal to the bandwidth for various doping levels. We find that the pairing interaction is well approximated by ${3/2}Ub(T)^2chi(K-K)$ with an effective temperature and doping dependent coupling $Ub(T)$ and the numerically calculated spin susceptibility $chi(K-K)$. We show that at low temperatures, $Ub$ may be accurately determined from a corresponding spin susceptibility based calculation of the single-particle self-energy. We conclude that the strength of the d-wave pairing interaction, characterized by the mean-field transition temperature, can be determined from a knowledge of the dressed spin susceptibility and the nodal quasiparticle spectral weight. This has important implications with respect to the questions of whether spin fluctuations are responsible for pairing in the high-T$_c$ cuprates.
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