Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model

TL;DR

This study uses ultracold atoms to observe charge and spin correlations in the 2D Fermi-Hubbard model, revealing how doping affects magnetic and charge interactions, with results aligning well with theoretical calculations.

Contribution

It provides the first site-resolved experimental observation of charge and spin correlations in the 2D Fermi-Hubbard model, demonstrating doping-dependent correlation behaviors.

Findings

Antiferromagnetic correlations peak at half-filling and decrease with doping.

Negative correlations between singly charged sites at large doping.

Positive correlations emerge at low doping, indicating doublon-hole bunching.

Abstract

Strong electron correlations lie at the origin of transformative phenomena such as colossal magneto-resistance and high-temperature superconductivity. Already near room temperature, doped copper oxide materials display remarkable features such as a pseudo-gap and a "strange metal" phase with unusual transport properties. The essence of this physics is believed to be captured by the Fermi-Hubbard model of repulsively interacting, itinerant fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. Correlations between singly charged sites are negative at large doping, revealing the Pauli and correlation hole\textemdash a suppressed probability of finding two fermions near each other. However, as the doping is reduced below a critical value, correlations between such local magnetic moments become positive, signaling strong bunching of doublons and holes. Excellent agreement with numerical linked-cluster expansion (NLCE) and determinantal quantum Monte Carlo (DQMC) calculations is found. Positive non-local moment correlations directly imply potential energy fluctuations due to doublon-hole pairs, which should play an important role for transport in the Fermi-Hubbard model.