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Nan Sheng

Nan Sheng contributes to research discovery and scholarly infrastructure.

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Published work

4 published item(s)

preprint2026arXiv

Agentic Discovery of Exchange-Correlation Density Functionals

The development of accurate exchange-correlation (XC) functionals remains a longstanding challenge in density functional theory (DFT). The vast majority of XC functionals have been hand designed by human researchers combining physical insight, exact constraints, and empirical fitting. Recent advances in large language models enable a systematic, automated alternative to this human-driven design loop. This report presents an agentic search system in which an LLM proposes structured functional-form changes guided by evolutionary history. The system attempts to improve functional performance through an iterative plan-execute-summarize loop, where improvements are measurable by optimizing functional parameters against a standard thermochemistry dataset, then evaluating performance on a held-out subset. The strongest discovered functional, SAFS26-a (Seed Agentic Functional Search 2026), improves upon the gold-standard ωB97M-V baseline by ~9%. These results also surface a cautionary lesson for AI-assisted science: models powerful enough to discover genuine improvements are equally capable of exploiting unphysical shortcuts to game the benchmark; domain expertise translated into explicitly enforced constraints remains essential to keeping results scientifically grounded.

preprint2022arXiv

Green's function formulation of quantum defect embedding theory

We present a Green's function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the $G_0 W_0$ approximation. We then show the robustness of our methodology by applying the theory with the newly derived scheme to several defects in diamond. Additionally, we discuss a strategy to obtain converged results as a function of the size and composition of the active space. Our results show that QDET is a promising approach to investigate strongly correlated states of defects in solids.

preprint2022arXiv

Partial Residuated Implications Derived from Partial Triangular Norms and Partial Residuated Lattices

In this paper, we reveal some relations between fuzzy logic and quantum logic, and mainly study the partial residuated implications (PRIs) derived from partial triangular norms (partial t-norms) and partial residuated lattices (PRLs), and expand some results in the article "material implication in lattice effect algebra". Firstly, according to the concept of partial triangular norms given by Borzooei, we introduce the connection between lattice effect algebra and partial t-norms, and prove that partial operations in any commutative quasiresiduated lattice are partial t-norms. Secondly, we give the general form of partial residuated implications and the concept of partial fuzzy implications (PFIs), and the condition that partial residuated implication is a fuzzy implication is given. We also prove that each partial residuated implication is a partial fuzzy implication. Thirdly, we propose the partial residuated lattice and study their basic properties, to discuss the corresponding relationship between PRLs and lattice effect algebras (LEAs), to further reveal the relationship between LEAs and residuated partial algebras. In addition, like the definition of partial t-norms, we also propose the concepts of partial triangular conorms (partial t-conorms) and corresponding partial co-residuated lattices (PcRLs). Finally, based on partial residuated lattices, we give the definition of well partial residuated lattices (wPRLs), study the filter of well partial residuated lattices, and then construct quotient structure of partial residuated lattices.

preprint2022arXiv

Quantum Embedding Theories to Simulate Condensed Systems on Quantum Computers

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate scale quantum computers using embedding theories, and we give examples for a specific class of materials, i.e., spin defects in solids. These are promising systems to build future quantum technologies, e.g., computers, sensors and devices for quantum communications. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.