Two-particle correlations in a dynamic cluster approximation with continuous momentum dependence: Superconductivity in the two-dimensional Hubbard model

Journal Article · Tue May 27 00:00:00 EDT 2014 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/physrevb.89.195133· OSTI ID:1565202

Staar, Peter ^[1]; Maier, Thomas ^[2]; Schulthess, Thomas C. ^[3]

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1. ETH Zurich, Zurich (Switzerland). Inst. for Theoretical Physics
2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
3. ETH Zurich, Zurich (Switzerland). Inst. for Theoretical Physics; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); ETH Zurich, Lugano (Switzerland). Swiss National Supercomputing Center

The DCA⁺ algorithm was recently introduced by Stear, Maier, and Schulthess [Phys. Rev. B 88, 115101 (2013), 10.1103/PhysRevB.88.115101] to extend the dynamic cluster approximation (DCA) with a continuous lattice self-energy in order to achieve better convergence with cluster size. In this work, we extend the DCA⁺ algorithm to the calculation of two-particle correlation functions by introducing irreducible vertex functions with continuous momentum dependence consistent with the DCA⁺ 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 ($$\textit{U}$$ =4$$\textit{t}$$) regime for large clusters. Here, we show that the new algorithm provides access to much larger clusters and delivers asymptotically converged results for $$T_c$$ for both the weak ($$\textit{U}$$ =4$$\textit{t}$$) and intermediate ($$\textit{U}$$ =7$$\textit{t}$$) coupling regimes, and thereby enables the accurate determination of the exact infinite cluster size result.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1565202
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 89, Issue 19; ISSN 1098-0121
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
materials science
physics