Mondragon-Shem Group

We develop theoretical tools for characterizing and engineering quantum matter, including phases defined by topology and symmetry protection. Our emphasis is on identifying structures that remain robust in realistic settings and support future quantum functionality.

Entanglement of Quantum Matter

We use entanglement to characterize many-body quantum matter. Entanglement spectra and entropies can diagnose hidden order, identify topological phases, and detect phase transitions. We develop entanglement-based tools for analyzing correlations, with particular emphasis on connections to quantum sensing.

Topological Insulators & Superconductors

We study topological phases in quantum many-body systems, with a focus on inhomogeneous topological phases. Our work uses topological invariants, Berry phases, and entanglement-based diagnostics to characterize topology in settings where spatial structure and disorder play an essential role. We also seek to understand Majorana modes in novel topological superconductors.