Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of d-wave pairing when a near neighbor Coulomb repulsion V is present in addition to the on-site Coulomb repulsion U . We find that d-wave pairing and the superconducting transition temperature Tc are only weakly suppressed as long as V does not exceed U/2. This stability is traced to the strongly retarded nature of pairing that allows the d-wave pairs to minimize the repulsive effect of V . When V approaches U/2, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of d-wave pairing and Tc than for smaller V .

We present the first open release of the DCA++ project, a high-performance research software framework to solve quantum many-body problems with cutting edge quantum cluster algorithms. DCA++ implements the dynamical cluster approximation (DCA) and its DCA + extension with a continuous self-energy. The algorithms capture nonlocal correlations in strongly correlated electron systems, thereby giving insight into high-T c superconductivity. The code's scalability allows efficient usage of systems at all scales, from workstations to leadership computers. With regard to the increasing heterogeneity of modern computing machines, DCA++ provides portable performance on conventional and emerging new architectures, such as hybrid CPU-GPU, sustaining multiple petaflops on ORNL's Titan and CSCS' Piz Daint supercomputers. Moreover, we show how sustainable and scalable development of the code base has been achieved by adopting standard techniques of the software industry. These include employing a distributed version control system, applying test-driven development and following continuous integration. PROGRAM SUMMARYProgram Title: DCA++ Licensing provisions: BSD-3-Clause Programming language: C++14 and CUDA Nature of problem: Understanding the fascinating physics of strongly correlated electron systems requires the development of sophisticated algorithms and their implementation on leadership computing systems. Solution method: The DCA++ code provides a highly scalable and efficient implementation of the dynamical cluster approximation (DCA) and its DCA + extension.Progress in solving the many-electron problem has been made by introducing models that comprise the fundamental mechanisms that lead to the observed phenomena. The two-dimensional Hubbard model, for instance, is believed to capture the important physics in the superconducting cuprates [1,2]. The Hubbard Hamiltonian describes fermions on a lattice, where the particles are allowed to hop between lattice sites and interact through Coulomb repulsion when they occupy the same site. Despite the simple structure, there exists no exact solution except for the one-dimensional case.To get insight into the physics described by the Hubbard model, one has to resort to numerical methods. Exact diagonalization (ED) and a variety of quantum Monte Carlo (QMC) algorithms solve the model on a finite-size lattice. While ED is restricted to small systems due to the exponential scaling of the problem size with the number of lattice sites, the negative sign problem prevents QMC calculations on large lattices or at low temperatures. Finite-size effects arise from the truncation of the infinite lattice to a finite number of sites.Mean-field theories choose a different approach and are formulated in the thermodynamic limit, that is on the infinite lattice. In dynamical mean-field theory (DMFT) [3] the infinite lattice problem becomes tractable by reducing it to the self-consistent solution of an effective impurity model. Underlying the single-site approximation is the assumption that the sel...

The dynamical cluster approximation (DCA) and its DCA + extension use coarse-graining of the momentum space to reduce the complexity of quantum many-body problems, thereby mapping the bulk lattice to a cluster embedded in a dynamical mean-field host. Here, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. While it gives a more localized self-energy for a given cluster size, we show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which converge to the results obtained from the standard coarse-graining with increasing cluster size. Most importantly, the new coarsegraining reduces the severity of the fermionic sign problem of the underlying quantum Monte Carlo cluster solver and thus allows for calculations on larger clusters. This enables the treatment of longerranged correlations than those accessible with the standard coarse-graining and thus can allow for the evaluation of the exact infinite cluster size result via finite size scaling. As a demonstration, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the extended DCA + algorithm permits the determination of the superconducting Tc on cluster sizes for which the results can be fit with a Kosterlitz-Thouless scaling law.

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Scientific discoveries across all fields, from physics to biology, are increasingly driven by computer simulations. At the same time, the computational demand of many problems necessitates large-scale calculations on high-performance supercomputers. Developing and maintaining the underlying codes, however, has become a challenging task due to a combination of factors. Leadership computer systems require massive parallelism, while their architectures are diversifying. New sophisticated algorithms are continuously developed and have to be implemented efficiently for such complex systems. Finally, the multidisciplinary nature of modern science involves large, changing teams to work on a given codebase. Using the example of the DCA++ project, a highly scalable and efficient research code to solve quantum many-body problems, we explore how computational science can overcome these challenges by adopting modern software engineering approaches. We present our principles for scientific software development and describe concrete practices to meet them, adapted from agile software development frameworks.