Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies

TL;DR

This paper develops a unified, non-perturbative framework connecting gapless fermionic systems with topological insulators in phase space, enabling direct derivation of their properties and responses without microscopic details.

Contribution

It introduces a general approach relating gapless fermions to topological insulators in phase space, applicable beyond non-interacting systems.

Findings

Established a direct relation between gapless fermions and phase-space topological insulators.

Derived low-energy response theories without microscopic assumptions.

Unified description of systems with Fermi surfaces, Berry phases, and nodal structures.

Abstract

We present a theory unifying the topological responses and anomalies of various gapless fermion systems exhibiting Fermi surfaces, including those with Berry phases, and nodal structures, which applies beyond non-interacting limit. As our key finding, we obtain a general approach to directly relate gapless fermions and topological insulators in phase space, including first- and higher-order insulators. Using this relation we show that the low-energy properties and response theories for gapless fermionic systems can be directly obtained without resorting to microscopic details. Our results provide a unified framework for describing such systems using well-developed theories from the study of topological phases of matter.