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

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 $U/t\gtrsim 6$ 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.

References in corpus (53)

• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Quantum Simulators: Architectures and Opportunities
• Tools for quantum simulation with ultracold atoms in optical lattices
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Short-range quantum magnetism of ultracold fermions in an optical lattice
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Site-resolved measurement of the spin-correlation function in the Hubbard model
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold fermions and the SU(N) Hubbard model
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Bad metallic transport in a cold atom Fermi-Hubbard system
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• String patterns in the doped Hubbard model
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Observation of canted antiferromagnetism with ultracold fermions in an optical lattice
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Spin Transport in a Mott Insulator of Ultracold Fermions
• An ytterbium quantum gas microscope with narrow-line laser cooling
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• A Short Introduction to Numerical Linked-Cluster Expansions
• Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Antiferromagnetic spin correlation of SU($\mathcal{N}$) Fermi gas in an optical super-lattice
• Doublon-hole correlations and fluctuation thermometry in a Fermi-Hubbard gas
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Topological liquids and valence cluster states in two-dimensional SU(N) magnets
• Parton theory of magnetic polarons: Mesonic resonances and signatures in dynamics
• Exact Diagonalization of Heisenberg SU(N) models
• Coupling a mobile hole to an antiferromagnetic spin background: Transient dynamics of a magnetic polaron
• Microscopic spinon-chargon theory of magnetic polarons in the t-J model
• Strong pairing in mixed dimensional bilayer antiferromagnetic Mott insulators
• Parton theory of ARPES spectra in anti-ferromagnetic Mott insulators
• Universal Thermometry for Quantum Simulation
• Thermodynamics of a bad metal-Mott insulator transition in the presence of frustration
• Flavour-selective localization in interacting lattice fermions via SU(N) symmetry breaking
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Magnetic ordering of three-component ultracold fermionic mixtures in optical lattices
• Dynamical formation of a magnetic polaron in a two-dimensional quantum antiferromagnet
• Critical entropies and magnetic-phase-diagram analysis of ultracold three-component fermionic mixtures in optical lattices
• Artificial $SU(3)$ Spin-Orbit Coupling and Exotic Mott Insulators
• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• Pairing of holes by confining strings in antiferromagnets
• Dominant fifth-order correlations in doped quantum anti-ferromagnets
• Finite Temperature Phase Transitions in the SU$(N)$ Hubbard model
• Interaction-driven topological phase transitions in fermionic SU($3$) systems
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Ferromagnetic ground state of SU(3) Hubbard model on the Lieb lattice
• Competing Charge and Magnetic Order in Fermionic Multi-Component Systems
• Discriminating antiferromagnetic signatures in ultracold fermions by tunable geometric frustration

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• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Coexisting Néel and charge density wave orders in attractive three-color fermions
• Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Solving the SU($N$) Orbital Hatsugai-Kohmoto Model
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Trion ordering in the attractive three-color Hubbard model on a $\pi$-flux square lattice
• $\mathrm{SU}(3)$ Fermi-Hubbard gas with three-body losses: symmetries and dark states
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Trion formation and ordering in the attractive SU(3) Fermi-Hubbard model