Vanishing spectral weight in a one-hole-doped antiferromagnet: A rigorous result

TL;DR

This paper rigorously demonstrates that in a one-hole-doped antiferromagnet, the phase string effect prevents spectral weight from appearing or causes hole localization, impacting understanding of doped Mott insulators.

Contribution

It provides a rigorous proof that the phase string effect cannot be removed by spin excitations, influencing spectral properties in the $t-J$ model.

Findings

Spectral weight $Z$ is zero due to phase string effects.

Hopping-induced phase string cannot be eliminated by low-energy spin excitations.

Doped holes tend to localize because of the phase string.

Abstract

By explicitly tracking the Marshall sign, a phase string induced by hopping is revealed in the one-hole-doped $t-J$ model. It is rigorously shown that such a phase string cannot be eliminated through low-lying spin excitations, and it either causes the spectral weight $Z=0$, or leads to the localization of the doped hole. Implications for finite doping are also discussed.