[Paper Review] Metal-insulator transition and magnetism of SU(3) fermions in the square lattice

Eduardo Ibarra-García-Padilla, Chunhan Feng+5 more|arXiv (Cornell University)|Jun 18, 2023

Physics of Superconductivity and MagnetismPhysics and Astronomy3 citations

TL;DR

This study investigates the SU(3) Fermi-Hubbard model at 1/3-filling on a square lattice using determinant quantum Monte Carlo (DQMC) and numerical linked-cluster expansion (NLCE). It identifies a metal-insulator transition at $U_c/t \sim 6$ and reveals a temperature-driven crossover from two-sublattice to three-sublattice antiferromagnetic order, with observable signatures in compressibility and spin-spin correlations, providing a roadmap for experimental detection in ultracold alkaline-earth atoms in optical lattices.

ABSTRACT

We study the SU(3) symmetric Fermi-Hubbard model (FHM) in the square lattice at $1/3$-filling using numerically exact determinant quantum Monte Carlo (DQMC) and numerical linked-cluster expansion (NLCE) techniques. We present the different regimes of the model in the $T-U$ plane, which are characterized by local and short-range correlations, and capture signatures of the metal-insulator transition and magnetic crossovers. These signatures are detected as the temperature scales characterizing the rise of the compressibility, and an interaction-dependent change in the sign of the diagonal spin-spin correlation function. The analysis of the compressibility estimates the location of the metal-insulator quantum critical point at $U_c/t \sim 6$, and provides a temperature scale for observing Mott physics at finite-$T$. Furthermore, from the analysis of the spin-spin correlation function we observe that for $U/t \gtrsim6$ and $T \sim J = 4t^2/U$ there is a development of a short-range two sublattice (2-SL) antiferromagnetic structure, as well as an emerging three sublattice (3-SL) antiferromagnetic structure as the temperature is lowered below $T/J \lesssim 0.57$. This crossover from 2-SL to 3-SL magnetic ordering agrees with Heisenberg limit predictions, and has observable effects on the density of on-site pairs. Finally, we describe how the features of the regimes in the $T$-$U$ plane can be explored with alkaline-earth-like atoms in optical lattices with currently-achieved experimental techniques and temperatures. The results discussed in this manuscript provide a starting point for the exploration of the SU(3) FHM upon doping.

Motivation & Objective

• To characterize the phase diagram of the SU(3) Fermi-Hubbard model at 1/3-filling in the T–U plane using numerically exact methods.
• To identify finite-temperature signatures of the metal-insulator quantum critical point and magnetic crossovers.
• To connect theoretical predictions with current experimental capabilities in ultracold alkaline-earth atoms in optical lattices.
• To analyze the emergence of short-range two-sublattice and three-sublattice antiferromagnetic order as a function of temperature and interaction strength.
• To provide a foundation for future studies of doped SU(3) Fermi-Hubbard systems at finite temperature.

Proposed method

• Employed determinant quantum Monte Carlo (DQMC) for numerically exact simulations of the SU(3) Fermi-Hubbard model on finite lattices.
• Applied numerical linked-cluster expansion (NLCE) to compute thermodynamic observables and spin-spin correlation functions.
• Used the compressibility as a probe to estimate the location of the metal-insulator quantum critical point.
• Analyzed the sign and temperature dependence of the diagonal spin-spin correlation function to detect magnetic crossovers.
• Performed finite-size scaling and Trotter error analysis to validate convergence and accuracy of DQMC results.
• Extracted the temperature scale $T^*$ from the derivative of the interaction energy $d(U\mathcal{D})/dT$, identifying a minimum at $T^*/t \sim 0.57J$.

Experimental results

Research questions

• RQ1 Where is the metal-insulator quantum critical point located in the T–U plane for the SU(3) Fermi-Hubbard model at 1/3-filling?
• RQ2 How does the spin-spin correlation function evolve with temperature, and what does it reveal about the nature of magnetic order?
• RQ3 What is the temperature scale at which a crossover from two-sublattice to three-sublattice antiferromagnetic order occurs?
• RQ4 How do finite-size effects and Trotter errors impact the reliability of the DQMC results at low temperatures and strong interactions?
• RQ5 Can the predicted phases and transitions be experimentally realized using current ultracold atom platforms with alkaline-earth-like atoms in optical lattices?

Key findings

• The metal-insulator quantum critical point is estimated at $U_c/t \sim 6$ based on the compressibility and the derivative of the interaction energy.
• A clear crossover from two-sublattice to three-sublattice antiferromagnetic order is observed at $T^*/t \sim 0.57J$, with $J = 4t^2/U$.
• For $U/t \gtrsim 6$, the diagonal spin-spin correlation function changes sign from positive to negative, signaling the onset of antiferromagnetic correlations.
• The density of on-site pairs $\mathcal{D}$ shows a low-temperature rise for $U > U_c$, consistent with Mott physics, with corrections from Trotter error less than 5%.
• Finite-size effects are small for $L \geq 10$ at $U/t = 8$, and the spin correlations are well converged for $T/t > 0.4$.
• The results are consistent with Heisenberg limit predictions and are experimentally accessible using current ultracold atom techniques with alkaline-earth-like atoms in optical lattices.