Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions

Abstract

Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU($N$) symmetry have provided important insights into many-body phenomena. However, these models have generally remained a theoretical idealization, since it is very difficult to exactly realize the SU($N$) symmetry in conventional quantum materials for large $N$. Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU($N$)-symmetric many-body models, where $N$ is tunable and can be as large as 10. This symmetry emerges due to the closed shell structure of AEAs, thereby leading to a perfect decoupling of the electronic degrees of freedom from the nuclear spin. In this work, we provide a systematic review of recent theoretical and experimental work on the many-body physics of these systems. We first discuss the thermodynamic properties and collective modes of trapped Fermi gases, highlighting the enhanced interaction effects that appear as $N$ increases. We then discuss the properties of the SU($N$) Fermi-Hubbard model, focusing on some of the major experimental achievements in this area. We conclude with a compendium highlighting some of the significant theoretical progress on SU($N$) lattice models and a discussion of some exciting directions for future research.

arXiv comment42 pages, 17 figures, 1 table

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Cited by in corpus (14)

• SU(N) magnetism with ultracold molecules
• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
• The SU(N) Fermi-Hubbard Model on two sites: Bethe Ansatz solution and Quantum Phase Transition of the Lipkin-Meshkov-Glick Model in the large-N limit
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Solving the SU($N$) Orbital Hatsugai-Kohmoto Model
• 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
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Quantum science with arrays of metastable helium-3 atoms
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU($N$) Fermi-Hubbard model
• Trion formation and ordering in the attractive SU(3) Fermi-Hubbard model
• $\mathrm{SU}(3)$ Fermi-Hubbard gas with three-body losses: symmetries and dark states
• Entanglement-enhanced correlation propagation in the one-dimensional SU($N$) Fermi-Hubbard model