Physics-informed Neural Quantum States for Strongly Correlated Matter

• Applicant: Dr. Robin Schäfer
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 575641691

We are witnessing a technological revolution driven by rapid advancement of neural networks and machine learning algorithms. While their presence in everyday life is already profound, their full potential for studying quantum many-body systems has yet to be determined. This proposal aims to leverage this development to investigate exotic quantum phases in condensed matter physics, focusing on two central challenges: (i) Topologically ordered states in two dimensions (ii) Quantum spin liquids in three-dimensional frustrated magnets. Both problems present significant challenges for established numerical methods such as the density matrix renormalization group and quantum Monte Carlo, each of which faces fundamental limitations in these contexts. The overarching goal of this project is to overcome these barriers through neural network–based algorithms — not only to advance the frontiers of computational physics, but also to gain new theoretical insights into these elusive quantum phases. Among the various applications of neural networks, neural quantum states offer a particularly promising avenue. They provide a variational ansatz for representing quantum many-body wave functions using only a polynomial number of parameters and are not subject to any known fundamental limitations. However, current applications still face significant challenges when confronted with non-trivial sign structures, as is the case in the proposed problems. To overcome these challenges, I propose developing physics-informed network architectures tailored to the structure of specific ground states. By incorporating physical insights directly into the network design, these architectures aim to improve both accuracy and convergence. With this proposal, I hope to bring methods based on neural quantum states closer to becoming a reliable, general-purpose tool for quantum many-body physics.

• DFG Programme: WBP Fellowship
• International Connection: USA
• Host: Professor Norman Yao, Ph.D.