Higher-Order Spin-Hole Correlations around a Localized Charge Impurity

TL;DR

This paper investigates how localizing a dopant in the 2D Hubbard model affects higher-order spin-charge correlations, revealing significant changes in magnetic dressing and correlation strengths, with implications for understanding doped Mott insulators.

Contribution

It provides a theoretical analysis of higher-order spin correlations near a localized charge impurity, extending experimental techniques to pinned dopants in the 2D Hubbard model.

Findings

Localization weakens connected third-order spin correlations for mobile holes.

Pinned dopants strengthen certain higher-order correlations compared to mobile ones.

Higher-order correlators remain observable at temperatures up to the spin-exchange energy J.

Abstract

Analysis of higher-order correlation functions has become a powerful tool for investigating interacting many-body systems in quantum simulators, such as quantum gas microscopes. Experimental measurements of mixed spin-charge correlation functions in the 2D Hubbard have been used to study equilibrium properties of magnetic polarons and to identify coherent and incoherent regimes of their dynamics. In this paper we consider theoretically an extension of this technique to systems which use a pinning potential to reduce the mobility of a single dopant in the Mott insulating regime of the 2D Hubbard model. We find that localization of the dopant has a dramatic effect on its magnetic dressing. The connected third-order spin correlations are weakened in the case of a mobile hole but strengthened near an immobile hole. In the case of the fifth-order correlation function, we find that its bare value has opposite signs in cases of the mobile and of fully pinned dopant, whereas the connected part is similar for both cases. We study suppression of higher-order correlators by thermal fluctuations and demonstrate that they can be observed up to temperatures comparable to the spin-exchange energy $J$. We discuss implications of our results for understanding the interplay of spin and charge in doped Mott insulators.