Abstract
The DCAalgorithm was recently introduced by Stear, Maier, and Schulthess [Phys. Rev. B 88, 115101 (2013)] to extend the dynamic cluster approximation (DCA) with a continuous lattice self-energy in order to achieve better convergence with cluster size. Here we extend the DCAalgorithm to the calculation of two-particle correlation functions by introducing irreducible vertex functions with continuous momentum dependence consistent with the DCAself-energy. This enables a significantly more controlled and reliable study of phase transitions than with the DCA. We test the new method by calculating the superconducting transition temperature in the attractive Hubbard model and show that it reproduces previous determinantal quantum Monte Carlo results. We then calculate in the doped repulsive Hubbard model, for which previous DCA calculations could only access the weak-coupling () regime for large clusters. We show that the new algorithm provides access to much larger clusters and delivers asymptotically converged results for for both the weak () and intermediate () coupling regimes, and thereby enables the accurate determination of the exact infinite cluster size result.
3 More- Received 18 February 2014
- Revised 30 April 2014
DOI:https://doi.org/10.1103/PhysRevB.89.195133
©2014 American Physical Society