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

References in corpus (15)

• High-temperature superconductivity in iron-based materials
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• 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
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Controlling and Detecting Spin Correlations of Ultracold Atoms in Optical lattices
• Exact Diagonalization of Heisenberg SU(N) models
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets

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• Solving the SU($N$) Orbital Hatsugai-Kohmoto Model
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