A self-energy-functional approach is applied to construct cluster approximations for correlated lattice models. It turns out that the cluster-perturbation theory [Phys. Rev. Lett. 84, 522 (2000)]] and the cellular dynamical mean-field theory [Phys. Rev. Lett. 87, 186401 (2001)]] are limiting cases of a more general cluster method. The results for the one-dimensional Hubbard model are discussed with regard to boundary conditions, bath degrees of freedom, and cluster size.

Based on the self-energy-functional approach proposed recently [M. Potthoff, Eur. Phys. J. B 32, 429 (2003)], we present an extension of the cluster-perturbation theory to systems with spontaneously broken symmetry. Our method applies to models with local interactions and accounts for both short-range correlations and long-range order. Short-range correlations are accurately taken into account via exact diagonalization of finite clusters. Long-range order is described by variational optimization of a ficticious symmetry-breaking field. In comparison with related cluster methods, our approach is more flexible and, for a given cluster size, less demanding numerically, especially at zero temperature. An application of the method to the antiferromagnetic phase of the Hubbard model at half-filling shows good agreement with results from quantum Monte-Carlo calculations. We demonstrate that the variational extension of the cluster-perturbation theory is crucial to reproduce salient features of the single-particle spectrum.

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Here and elsewhere, certain product names may be the property of their respective third parties.xxii ■ IntroduCtIon Use Interprocedural OptimizationAdd the compiler flag -ipo to switch on interprocedural optimization. This will give the compiler a holistic view of the program and open more optimization opportunities for the program as a whole. Note that this will also increase the overall compilation time.Runtime profiling can also increase the chances for the compiler to generate better code. Profile-guided optimization requires a three-stage process. First, compile the application with the compiler flag -prof-gen to instrument the application with profiling code. Second, run the instrumented application with a typical dataset to produce a meaningful profile. Third, feed the compiler with the profile (-prof-use) and let it optimize the code.

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