Cluster approximation for an infinite-dimensional determinant

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.

Michigan State University

T. A. Kaplan, Petros N. Argyres

Romuald L yżwa, Zbigniew Domański

Ground-state properties of the asymmetric Hubbard model are studied on one-dimensional clusters (rings) with N=6, 8, and 10 sites. The ground-state energy, correlation functions, and phase diagrams are determined for various sets of model parameters. Computations are performed both by exact diagonalization (for N=6) and by an approximate method by which correlation effects can be examined on larger clusters than exact diagonalization allows. In the limiting cases (one limit corresponds to the spinless Falicov-Kimball model and the other to the Hubbard model) our results agree quite well with those obtained analytically for infinite systems.

Stefano Zippilli, David Vitali

Gaussian cluster states are ideal infinitely squeezed states. In practice it is possible to construct only approximated version of them with finite squeezing. Here we show how to determine the specific multimode squeezing transformation, which generates a faithful approximation of any given Gaussian cluster state.

J. P. Hague