The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite-cluster methods typically indicate that stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides an opportunity to study the influence of fluctuating stripe correlations on the model’s pairing correlations within a unified numerical framework. Using this approach, we also find evidence for pair-density-wave correlations whose strength is correlated with that of the stripes.

The nature and mechanism of superconductivity in the extremely electron-doped FeSe based superconductors continues to be a matter of debate. In these systems, the hole-like band has moved below the Fermi energy, and various spin-fluctuation theories involving pairing between states near the electron Fermi surface and states of this incipient band have been proposed. Here, using a dynamic cluster quantum Monte Carlo calculation for a bilayer Hubbard model we show that the pairing in these systems can be understood in terms of an effective retarded attractive interaction between electrons near the electron Fermi surface.

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The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO2 planes. Here, we use a dynamical cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.

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.