Shi studied fractionalization in frustrated quantum matter, where the interacting spins are unable to order. Instead, they create long-range patterns of entanglement leading to states of matter such as quantum spin liquids, heralding the topological quantum matter with novel fractionalized particles and emergent gauge fields. These states are characterized by topological order: ground state degeneracy on a manifold of non-zero genus, and fractionalized excitations with abelian and non-abelian quantum statistics. In these states, the original localized spin degrees undergo further fractionalization to give new degrees of freedom, such as Majorana fermions and spinons. In these states, both charges and spins are localized. However, the emergent fractionalized degrees of freedom can be remarkably delocalized and able to transport energy. Identifying and studying the phenomena of fractionalization presents a dual challenge: discerning fractionalized particles and finding material candidates that realize fractionalization. His dissertation presents a comprehensive theoretical study of fractionalization in both one and two dimensions, focusing on these challenges. [Link to his dissertation]

Joseph studied the Fermi-Hubbard model, a theoretical model that captures the insulating and conducting phases of high temperature superconducting materials, where he characterized novel quantum phases and dynamics realized on cutting-edge quantum simulation platforms. By correlating maps of the local density of states, the local magnetization, and the local bond conductivity, he found a collapse of the Mott gap toward a V-shape pseudo-gapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites, while the electronic bond conductivity increases. His results provide one of the first microscopic investigations of dynamical response and how these two phases (correlated metal and Mott insulator) coexist microscopically and lead to an overall macroscopic phase transition. Expanding beyond the ground state properties of interacting matter, he also venture exploring the field of nonequilibrium quantum dynamics that bridges foundational atomic, molecular, and optical and condensed matter models. In relevant works he presented a new framework that connects physical spin-fluctuations, quantum Fisher information, and bipartite entanglement entropy between collective quantum systems.

In Franz’s work he presented an analysis of the magnetic anisotropy that enables 2D ferromagnetism in CrI₃ , one of the first 2D ferromagnets discovered. He determined the most general microscopic spin interactions allowed by this material’s crystal symmetries and estimate the strength and sign of these interactions by fitting angle-dependent ferromagnetic resonance data using this spin model. He also presented a symmetry analysis of the most general forms of tensors describing physical responses in 2D materials composed of a honeycomb lattice of edge-sharing octahedra relevant for the aforesaid materials. [Link to his thesis]

Wenjuan’s research focuses how the interplay between strong correlations and spin-orbit coupling gives rise to unconventional magnetic structures with unusual properties, where both the orbital and spin orderings dictate the nature of magnetism. Since orbitals are directional and couple to the lattice, magnetism in these materials can be manipulated by external strain, providing a new knob to tune their magnetic properties. [Link to her thesis]