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.

42 pages, 17 figures, 1 table

References in corpus (69)

• Many-Body Physics with Ultracold Gases
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• The Hubbard Model
• Tools for quantum simulation with ultracold atoms in optical lattices
• A one-dimensional liquid of fermions with tunable spin
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• 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
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Spin-orbital quantum liquid on the honeycomb lattice
• Doublon-hole correlations and fluctuation thermometry in a Fermi-Hubbard gas
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice
• Exact Diagonalization of Heisenberg SU(N) models
• State-dependent, addressable subwavelength lattices with cold atoms
• Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models
• Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
• Determination of the 5d6s 3D1 state lifetime and blackbody radiation clock shift in Yb
• Thermodynamics of a deeply degenerate SU($N$)-symmetric Fermi gas
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields
• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
• Flavour-selective localization in interacting lattice fermions via SU(N) symmetry breaking
• Local readout and control of current and kinetic energy operators in optical lattices
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures
• Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices
• Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model
• Synthetic dimensions for topological and quantum phases: Perspective
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Metal-insulator transition and magnetism of SU(3) fermions in the square lattice
• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators
• Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• A strontium quantum-gas microscope
• Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting SU($2N$) Dirac fermions
• Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium
• Quantum Quench and Charge Oscillations in the SU(3) Hubbard Model: a Test of Time Evolving Block Decimation with general non-Abelian Symmetries
• SU(N) magnetism with ultracold molecules
• Breaking of SU(4) symmetry and interplay between strongly correlated phases in the Hubbard model
• Resonant dynamics of strongly interacting SU($n$) fermionic atoms in a synthetic flux ladder
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure
• Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators
• SU(4)-symmetric Hubbard model at quarter filling: Insights from the dynamical mean-field approach
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Itinerant ferromagnetism in dilute SU(N) Fermi gases
• SU(N) Fermi liquid at finite temperature
• Scalable, ab initio protocol for quantum simulating SU($N$)$\times$U(1) Lattice Gauge Theories
• Itinerant Ferromagnetism in SU(N)-Symmetric Fermi Gases at Finite Temperature: First Order Phase Transitions and Time-Reversal Symmetry
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz
• Orbital ordering of ultracold alkaline-earth atoms in optical lattices
• Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• Engineering of a Low-Entropy Quantum Simulator for Strongly Correlated Electrons Using SU($\mathcal{N}$)-Symmetric Cold Atom Mixtures
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Beyond universality in repulsive SU(N) Fermi gases
• Spectroscopic evidence for engineered hadron formation in repulsive fermionic $\text{SU}(N)$ Hubbard Models
• Quantum phases of collective SU(3) spin systems with bipartite symmetry
• On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models
• Sub-dimensional magnetic polarons in the one-hole doped SU(3) $t$-$J$ model

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