# Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model

## TL;DR

This paper investigates magnetic fluctuations in the two-dimensional repulsive Fermi Hubbard model near half-filling, identifying the temperature scales and interaction strengths where magnetic correlations are most prominent, relevant for cold atom experiments.

## Contribution

The study employs a self-consistent diagrammatic approach to quantify magnetic fluctuation temperature scales and their dependence on doping and interaction strength in the Hubbard model.

## Key findings

- Maximum magnetic fluctuations occur at U/t ≈ 4-6.
- The characteristic temperature T_M(n) varies with doping levels.
- Magnetic fluctuations are strongest near U/t ≈ 4-6, facilitating experimental observation.

## Abstract

The repulsive Fermi Hubbard model on the square lattice has a rich phase diagram near half-filling (corresponding to the particle density per lattice site $n=1$): for $n=1$ the ground state is an antiferromagnetic insulator, at $0.6 < n \lesssim 0.8$, it is a $d_{x^2-y^2}$-wave superfluid (at least for moderately strong interactions $U \lesssim 4t$ in terms of the hopping $t$), and the region $1-n \ll 1$ is most likely subject to phase separation. Much of this physics is preempted at finite temperatures and to an extent driven by strong magnetic fluctuations, their quantitative characteristics and how they change with the doping level being much less understood. Experiments on ultra-cold atoms have recently gained access to this interesting fluctuation regime, which is now under extensive investigation. In this work we employ a self-consistent skeleton diagrammatic approach to quantify the characteristic temperature scale $T_{M}(n)$ for the onset of magnetic fluctuations with a large correlation length and identify their nature. Our results suggest that the strongest fluctuations---and hence highest $T_{M}$ and easiest experimental access to this regime---are observed at $U/t \approx 4-6$.