Exploring Global Anomalies in Quantum Systems

Recent research by Lei Su and Ivar Martin, titled "Global anomalies of Green's function zeros," explores the implications of global anomalies in systems characterized by symmetry-preserving Luttinger surfaces. These surfaces represent the manifolds of fermionic Green's function zeros in momentum space at zero energy. The authors utilize nonlocal effective theories, which arise from integrating out low-energy states, to analyze the simplest Lagrangian that describes a gapless Dirac zero and a two-pole variant. They discuss the global anomalies associated with these models and the concept of bulk-boundary correspondence.

The study emphasizes the constraints on potential phases that exhibit Green's function zeros of Dirac type, including non-Fermi liquids and emergent gapless quasiparticles on Luttinger surfaces. The findings provide insights into the behavior of quantum systems under specific conditions, which could have broader implications for understanding complex materials and phenomena in condensed matter physics.

This work contributes to the ongoing discourse in quantum physics, particularly regarding the nature of anomalies in topological systems and their relevance to nonperturbative physics. The authors suggest that their analysis could pave the way for further research into the properties of materials that exhibit similar anomalies, potentially influencing future developments in quantum materials and technologies.

The paper can be cited as follows: Su, L., & Martin, I. (2024). Global anomalies of Green's function zeros. arXiv:2405.08093.