Hubbard models on general lattices: A dynamical cluster approximation approach

Christopher N. Varney, Richard T. Scalettar, Mark Jarrell +2 more

Alexandru Macridin, Mark Jarrell, Thomas Maier +1 more

Karan Aryanpour, Matthias H. Hettler

Hunpyo Lee, Yu‐Zhong Zhang, Harald O. Jeschke +2 more

Peter Staar, Thomas Maier, T. C. Schulthess

The DCA${}^{+}\phantom{\rule{0.222222em}{0ex}}$algorithm 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 DCA${}^{+}\phantom{\rule{0.222222em}{0ex}}$algorithm to the calculation of two-particle correlation functions by introducing irreducible vertex functions with continuous momentum dependence consistent with the DCA${}^{+}\phantom{\rule{0.222222em}{0ex}}$self-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 ${T}_{c}$ in the attractive Hubbard model and show that it reproduces previous determinantal quantum Monte Carlo results. We then calculate ${T}_{c}$ in the doped repulsive Hubbard model, for which previous DCA calculations could only access the weak-coupling ($U=4t$) regime for large clusters. We show that the new algorithm provides access to much larger clusters and delivers asymptotically converged results for ${T}_{c}$ for both the weak ($U=4t$) and intermediate ($U=7t$) coupling regimes, and thereby enables the accurate determination of the exact infinite cluster size result.

J. Monecke