Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model

Abstract

Mott insulators are paradigms of strongly correlated physics, giving rise to phases of matter with novel and hard-to-explain properties. Extending the typical SU(2) symmetry of Mott insulators to SU($N$) is predicted to give exotic quantum magnetism at low temperatures, but understanding the effect of strong quantum fluctuations for large $N$ remains an open challenge. In this work, we experimentally observe nearest-neighbor spin correlations in the SU(6) Hubbard model realized by ytterbium atoms in optical lattices. We study one-dimensional, two-dimensional square, and three-dimensional cubic lattice geometries. The measured SU(6) spin correlations are dramatically enhanced compared to the SU(2) correlations, due to strong Pomeranchuk cooling. We also present numerical calculations based on exact diagonalization and determinantal quantum Monte Carlo. The experimental data for a one-dimensional lattice agree with theory, without any fitting parameters. The detailed comparison between theory and experiment allows us to infer from the measured correlations a lowest temperature of $\left[0.096\pm 0.054(\mathrm{theory})\pm 0.030(\mathrm{experiment})\right]/k_{\mathrm{B}}$ times the tunneling amplitude. For two- and three-dimensional lattices, experiments reach entropies below where our calculations converge, highlighting the experiments as quantum simulations. These results open the door for the study of long-sought SU($N$) quantum magnetism.

13 pages, 8 figures

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• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
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• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices
• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets

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• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
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• Spin exchange-enabled quantum simulator for large-scale non-Abelian gauge theories
• Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice
• Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators
• Trion states and quantum criticality of attractive SU(3) Dirac fermions
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• SU($N$) altermagnetism: Lattice models, magnon modes, and flavor-split bands
• Hubbard parameters for programmable tweezer arrays
• Synthetic high angular momentum spin dynamics in a microwave oscillator
• Splitting and connecting singlets in atomic quantum circuits
• Engineering the Kondo impurity problem with alkaline-earth atom arrays
• Engineering of a Low-Entropy Quantum Simulator for Strongly Correlated Electrons Using SU($\mathcal{N}$)-Symmetric Cold Atom Mixtures
• SU($N$) symmetry with ultracold alkali dimers: weak dependence of scattering properties on hyperfine state
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
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• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
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• Measuring the nuclear magnetic quadrupole moment of optically trapped ytterbium atoms in the metastable state
• Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices
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• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Static impurity in a mesoscopic system of SU($N$) fermionic matter-waves
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Quantum science with arrays of metastable helium-3 atoms
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Solving the SU($N$) Orbital Hatsugai-Kohmoto Model
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Entanglement spectra of non-chiral topological (2+1)-dimensional phases with strong time-reversal breaking, Li-Haldane state counting, and PEPS
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• Nonzero angular momentum density wave phases in SU($N$) fermions with singlet-bond and triplet-current interactions
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• Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS
• Optimal Work Extraction from Finite-Time Closed Quantum Dynamics
• Entanglement-enhanced correlation propagation in the one-dimensional SU($N$) Fermi-Hubbard model
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• The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
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