Signatures of Green's function zeros and their topology using impurity spectroscopy

TL;DR

This paper demonstrates that Green's function zeros, which encode topological properties in Mott insulators, can be detected via impurity spectroscopy, revealing in-gap states called 'zerons' that vanish under certain magnetic fields.

Contribution

It provides a theoretical framework linking Green's function zeros to observable impurity spectral features, supported by exact solutions and mapping to doped Mott insulators.

Findings

Green's function zeros manifest as in-gap spectral weight

Zeron excitations are localized doublons or holons

Zero spectral weight vanishes above a critical Zeeman field

Abstract

Topology without quasiparticles has emerged as a key framework for understanding Mott insulators, where Green's-function zeros encode nontrivial topological structure. Yet, experimental detection of these zeros represents a challenge. Using exact diagonalization of the one-dimensional Hubbard model with an impurity and Zeeman field, supported by exact analytic results, we show that Green's-function zeros manifest as an in-gap spectral weight in the unitary scattering regime. In this limit, we map the impurity problem onto a doped Mott insulator and identify the resulting in-gap state as a "zeron" excitation which is a localized doublon (holon) for an attractive (repulsive) potential. The zeron spectral weight and its associated zero vanish above a critical Zeeman field. Our results imply that Green's function zeros have in fact already been observed in experiments, and establish impurity and magnetic-field tuning as practical tools for controlling their topology.