Global anomalies of Green's function zeros

TL;DR

This paper investigates the global anomalies associated with Green's function zeros in strongly interacting fermionic systems, focusing on their topological and symmetry properties, and implications for non-Fermi liquid phases.

Contribution

It introduces a nonlocal effective theory for Green's function zeros, analyzes global anomalies and bulk-boundary correspondence, and discusses constraints on phases with symmetry preservation.

Findings

Global anomalies constrain phases with Green's function zeros.

Spontaneous symmetry breaking is necessary to avoid unstable GFZs.

Nonlocal fermionic theories may not support symmetric gapped phases.

Abstract

We study global anomalies of nonlocal effective theories proposed to describe symmetry-preserving Luttinger surfaces, i.e., the momentum-space manifolds of Green's function zeros (GFZs) at zero energy, in strongly interacting fermionic systems. In particular, we focus on simplest possible cases associated with a gapless Dirac zero, which is the counterpart of the gapless Dirac quasiparticle in weakly interacting systems. These theories may be derived by integrating out low-energy degrees of freedom that do not couple to the relevant gauge field. We discuss the global anomaly, the bulk-boundary correspondence, and the constraint on phases consistent with the anomaly, such as non-Fermi liquids and emergent gapless quasiparticles on Luttinger surfaces. Failing to avoid a spontaneous symmetry breaking in the thermodynamical limit inevitably leads unstable GFZs. We also provide some perspectives on why the related nonlocal fermionic effective theory studied recently is not a suitable starting point for a symmetrically gapped phase.