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

• URL: http://arxiv.org/abs/2306.10644v2
• Date: Tue, 26 Sep 2023 21:46:53 GMT
• Title: Metal-insulator transition and magnetism of SU(3) fermions in the square lattice
• Authors: Eduardo Ibarra-Garc\'ia-Padilla, Chunhan Feng, Giulio Pasqualetti, Simon F\"olling, Richard T. Scalettar, Ehsan Khatami, Kaden R. A. Hazzard
• Abstract summary: We study the SU(3) symmetric Fermi-Hubbard model (FHM) in the square lattice at $1/3$-filling. We present the different regimes of the model in the $T-U$ plane, which are characterized by local and short-range correlations. We describe how the features of the regimes in the $T$-$U$ plane can be explored with alkaline-earth-like atoms in optical lattices.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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