# Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model

## TL;DR

This study investigates the evolution of spin and charge correlations across the metal-insulator transition in the half-filled 2D Hubbard model, revealing distinct temperature-dependent regimes and emphasizing the role of non-local fluctuations.

## Contribution

It provides controlled diagrammatic Monte Carlo results detailing the crossover from metallic to insulating behavior, highlighting the significance of non-local correlations and local magnetic moments.

## Key findings

- Charge and spin correlations change qualitatively at different temperature scales.
- An intermediary non-Fermi-liquid regime with local moments is identified.
- Results are relevant for ultracold atom experiments.

## Abstract

The $2d$ Hubbard model with nearest-neighbour hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using diagrammatic Monte Carlo in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the crossover are observed at well-separated temperature scales, which encase the intermediary regime of non-Fermi-liquid character, where local magnetic moments are formed and non-local fluctuations in both channels are essential.