UC San Diego

In this thesis, I will present mainly three directions of research: symmetric mass genera- tion (SMG), anomaly-constrained gapless quantum phases, and unconventional superconductivity. SMG is a new mass generation mechanism through strong interactions that preserve the symme- tries, different from the conventional Yukawa-Higgs mechanism. I will discuss its applications in chiral lattice gauge theory, symmetric gapping of Fermi liquids, Green’s function properties and the corresponding optical responses of SMG insulators. Then I will discuss about emergent anomalies in many-body systems, and its implications for low-energy phases. In particular, we will see how gapless symmetry protected topological phases and symmetry-enriched topological ordered phases can arise through through effective partial gauging. Last but not least, for the unconventional superconductivity part, I will focus on the exotic time-reversal symmetry breaking normal state of multi-gap superconductors, and the stabilization and topology of superconductors with pairings involving multiple orbitals.