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

Publication Date

1-1-2023

Document Type

Article

Publication Title

Physical Review A

Volume

108

Issue

5

DOI

10.1103/PhysRevA.108.053312

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 and numerical linked-cluster expansion 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 Uc/t∼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≳6 and T∼J=4t2/U there is a development of a short-range two-sublattice (2SL) antiferromagnetic structure, as well as an emerging three-sublattice (3SL) antiferromagnetic structure as the temperature is lowered below T/J≲0.57. This crossover from 2SL to 3SL 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 paper provide a starting point for the exploration of the SU(3) FHM upon doping.

Funding Number

995764

Funding Sponsor

National Science Foundation

Department

Physics and Astronomy

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