Strongly correlated quantum materials exhibit extraordinary emergent phenomena, such as unconventional superconductivity, metal-insulator transitions, and strain-tunable phases. These properties arise from complex, nonlinear interactions between electronic correlations and lattice degrees of freedom. Standard computational approaches, like Density Functional Theory (DFT), fail to describe these systems at finite temperatures. Meanwhile, advanced methods like Dynamical Mean-Field Theory (DMFT) lack vital lattice and mechanical capabilities, including stress tensors and momentum-resolved electron-phonon interactions. Because of these limitations, scientists cannot accurately predict correlation-driven phase stability and strain-engineered superconductivity.

To solve this problem, this project will elevate DFT+embedded DMFT (DFT+eDMFT) into a comprehensive, predictive framework that treats electronic correlations, lattice dynamics, and mechanical responses on equal footing. This objective will be achieved through three integrated goals: developing new DMFT-based methods to calculate temperature-dependent electron-phonon interaction; deriving analytic stress and strain tensors for self-consistent structural optimization; and integrating these tools into a scalable, open-source software platform under the Apache License 2.0. The framework will be applied to representative correlated superconductors, specifically infinite-layer nickelates and iron-based systems, to understand how correlations and phonons control superconductivity.

This project will deliver first-of-their-kind computational capabilities to close the gap between electronic correlations and lattice mechanics. Ultimately, the resulting open-source software will empower researchers to predictively design, manipulate, and control novel quantum properties under realistic thermodynamic and strain conditions, directly strengthening the computational materials ecosystem.