• Strongly Correlated Systems

Strongly correlated systems usually refers to electronic materials which cannot be understood through energy band theories with single electron picture. The minimum model of these systems is the celebrated Hubbard model, which captures both the electron hopping and strong Coulomb repulsion. A lot of analytical and numerical tools have been developed for strongly correlated electronic systems. 

I believe that advancing numerical simulation methods for correlated systems is a central objective in modern condensed matter physics. My broader research interest lies in numerical approaches and non-perturbative properties in strongly correlated systems.

• Recent relevant publications

• F Xie, Y Fang, Y Li, Y Huang, L Chen, C Setty, S Sur, B Yakobson, R Valentí, Q Si, Phys. Rev. Research 7, L022061 (2025)

• C Setty, F Xie, S Sur, L Chen, MG Vergniory, Q Si, Phys. Rev. Research 6, 033235 (2024)

• C Setty, S Sur, L Chen, F Xie, H Hu, S Paschen, J Cano, Q Si, Phys. Rev. Research 6 (3), L032018 (2024)

• Topological Band Theories

Topological band theory has revolutionized our understanding of solid state systems. Even in the absence of Coulomb interactions between electrons, the complex pattern of electrons hopping can make their wave function "wind" over itself, leading to exotic physical phenomena, including the astonishing quantization of Hall conductivity. These exotic wave functions can also affect how these electrons interact with each other.

I am also interested in the relationship between topological bands and symmetries, as well as their potential connection to electron interactions.

• Recent relevant publications

• F Xie, Y Fang, L Chen, J Cano, Q Si, arXiv: 2407.08920 (2024)

• Moiré Materials

Both superconducting and correlated insulating phases have been discovered in twisted bilayer graphene (TBG) in 2018. Since then, the moiré materials have been considered as ideal tunable platforms for studying the interplay between topology and strong correlation. Some of the phenomena observed in these systems are hard to realized or control in traditional crystalline materials. 

I am interested in the theoretical modeling for various types of moiré systems, using the techniques and theories from both strong correlation and topological band theories.

• Recent relevant publications

• F Xie, L Chen, Y Fang, Q Si, Phys. Rev. Research 7, 033093 (2025)

• F Xie, L Chen, S Sur, Y Fang, J Cano, Q Si, Phys. Rev. Lett. 134, 136503 (2025)

• F Xie, C Li, J Cano, Q Si, arXiv: 2503.21769 (2025)

• F Xie, L Chen, Q Si, Phys. Rev. Research 6 (1), 013219 (2024)