| We compare the accuracy of two cluster extensions of dynamical mean-field theory in describing d-wave superconducting pairing, using as a reference model the saddle-point t-J model, for which an exact solution is available in the thermodynamic (i.e., infinite cluster) limit. The model provides as well a good qualitative description of the properties of high-temperature superconductors. The two methods are the cellular dynamical mean-field theory, which is based on a real-space perspective, and the dynamical cluster approximation, which enforces a momentum-space picture. We consider the scaling of the two methods for large cluster sizes, but we also focus on the behavior for small clusters, such as those accessible by means of present techniques, with particular emphasis on the geometrical structure, which we find to be a particularly relevant issue in small clusters. |
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