Elements: Efficient open-source packages for non-perturbative simulations of electron-phonon interactions in quantum materials

Strongly correlated quantum materials realize a wide range of novel phases of matter and functional properties that result from the quantum many-body interactions between their constitute electrons and atoms. While these materials have tremendous transformative potential across nearly all science and technology sectors, they are incredibly challenging to model using conventional theoretical approaches. Progress in understanding and predictive capabilities for many of these materials has thus primarily been achieved with powerful numerical methods capable of simulating their complex quantum many-body dynamics. Efforts in this area have focused mainly on cyberinfrastructure for materials with strong electron-electron interactions. However, interactions between electrons and the motion of material atoms (the so-called electron-phonon interaction) also play a crucial role in several families of quantum materials, while the cyberinfrastructure for simulating such systems has remained underdeveloped. This project fills this gap by developing two new packages for performing state-of-the-art quantum Monte Carlo simulations of diverse models with realistic electron-phonon interactions. These packages leverage recent advances in sampling methods to enable simulations of physically realistic models for the first time. These packages are being developed and maintained as part of the SmoQySuite organization (https://github.com/SmoQySuite), prioritizing the creation of flexible and easy-to-use many-body codes while maintaining excellent performance. By providing new and flexible tools for simulating generalized electron-phonon coupled models, this project will enable new research into the role this interaction plays across a wide range of quantum materials. In addition to providing new scientific capabilities, this cyberinfrastructure will reduce the barrier to entry into computational materials research and promote reproducibility in quantum materials research. Finally, the SmoQySuite organization will host workshops and create tutorials for these codes, helping to grow a community of users and developers to disseminate our codes more broadly.Understanding and predicting the properties of quantum materials remains at the forefront of condensed matter physics and materials science research. The strong electron-electron and electron-phonon interactions in these materials can produce a highly correlated electron liquid that often defies conventional single-particle descriptions. Therefore, modeling for these materials frequently relies on nonperturbative numerical methods, which has motivated the development of many open-source codes for simulating correlated models for quantum materials. However, many of these tools cannot treat electron-phonon interactions, or if they can, they are limited to unphysical parameter regimes where the phonon’s energy is comparable to or larger than the nearest-neighbor electronic hopping. This project is closing this critical cyber infrastructure gap by developing SmoQyElPhQMC.jl and SmoQyDCA.jl, two open-source and user-friendly software packages for performing state-of-the-art quantum Monte Carlo (QMC) simulations of electron-phonon coupled systems. These packages leverage recent advances in hybrid Monte Carlo (HMC) sampling methods. This approach significantly reduces autocorrelation times and overall computational cost, enabling simulations of a broad general class of electron-phonon interactions with physically realistic low-energy optical and even acoustic phonon branches. The SmoQyElPhQMC.jl package targets uncorrelated electron-phonon Hamiltonians and combines HMC with several other algorithmic advances to perform scalable nonperturbative sign-problem-free QMC simulations with a computational complexity that is approximately linear in both system size and inverse temperature. Conversely, SmoQyDCA.jl package targets correlated models, where the fermion sign problem is mitigated by self-consistently embedding a cluster in a mean field within the dynamical cluster approximation. In this case, SmoQyDCA.jl will use determinant quantum Monte Carlo with HMC sampling of the phonon degrees of freedom as the cluster solver to achieve efficient scaling while retaining the ability to treat realistic electron-phonon interactions. These packages are being developed as part of the SmoQySuite organization (https://github.com/SmoQySuite). This platform prioritizes creating many-body codes that are flexible and easy-to-use while retaining high performance levels. In addition to providing new scientific capabilities, developing this cyberinfrastructure will help reduce the barrier to entry into computational materials research for new and established researchers. The SmoQySuite organization will host workshops and create tutorials for these codes, helping to grow a community of users and developers to disseminate our codes more broadly.This award by the NSF Office of Advanced Cyberinfrastructure is jointly supported by the Division of Materials Research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.