Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets

Antiferromagnetic Spin Correlation of SU(N) Fermi Gas in an Optical Superlattice

Large-spin cold atomic systems can exhibit unique phenomena that do not appear in spin-1/2 systems. We report the observation of nearest-neighbor antiferromagnetic spin correlations of a Fermi gas with SU(N) symmetry trapped in an optical lattice. The precise control of the spin degrees of freedom provided by an optical pumping technique enables us a straightforward comparison between the cases of SU(2) and SU(4). Our important finding is that the antiferromagnetic correlation is enhanced for the SU(4)-spin system compared with SU(2) as a consequence of a Pomeranchuk cooling effect. This work is an important step towards the realization of novel SU(N>2) quantum magnetism.

Interaction Effects with Varying N in SU(N) Symmetric Fermion Lattice Systems

The interaction effects in ultracold Fermi gases with SU(N) symmetry are studied nonperturbatively in half filled one-dimensional lattices by employing quantum Monte Carlo simulations. We find that, as N increases, weak and strong interacting systems are driven to a crossover region, but from opposite directions as a convergence of itinerancy and Mottness. In the weak interaction region, particles are nearly itinerant, and interparticle collisions are enhanced by N, resulting in the amplification of interaction effects. In contrast, in the strong coupling region, increasing N softens the Mott-insulating background through the enhanced virtual hopping processes. The crossover region exhibits nearly N-independent physical quantities, including the relative bandwidth, Fermi distribution, and the spin structure factor. The difference between even-N and odd-N systems is most prominent at small N's with strong interactions, since the odd case allows local real hopping with an energy scale much larger than the virtual one. The above effects can be experimentally tested in ultracold atom experiments with alkaline-earth(-like) fermions such as ^{87}Sr (^{173}Yb).

Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S=1/2 antiferromagnets using the basis of spin eigenstates of clusters to avoid the severe sign problem faced by other QMC methods. We demonstrate the utility of the method in several cases with competing exchange interactions and flag important limitations as well as possible extensions of the method.

Magnetic crystals and helical liquids in alkaline-earth fermionic gases

The joint action of a magnetic field and of interactions is crucial for the appearance of exotic quantum phenomena, such as the quantum Hall effect. Owing to their rich nuclear structure, equivalent to an additional synthetic dimension, one-dimensional alkaline-earth(-like) fermionic gases with synthetic gauge potential and atomic contact repulsion may display similar related properties. Here we show the existence and the features of a hierarchy of fractional insulating and conducting states by means of analytical and numerical methods. We demonstrate that the gapped states are characterized by density and magnetic order emerging solely for gases with effective nuclear spin larger than 1/2, whereas the gapless phases can support helical modes. We finally argue that these states are related to an unconventional fractional quantum Hall effect in the thin-torus limit and that their properties can be studied in state-of-the-art laboratories.

Quantum critical spin-2 chain with emergent SU(3) symmetry

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Ultracold Fermi gases with emergent SU(N) symmetry

We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, (3) the realization of a Mott insulator of (173)Yb atoms, (4) the creation of various kinds of Fermi-Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.

Exact Diagonalization of Heisenberg SU(N) models

Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on n sites increases very fast with N, this formulation allows us to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).

Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning-field quantum Monte Carlo simulations

We nonperturbatively investigate the ground state magnetic properties of the 2D half-filled SU(2N) Hubbard model in the square lattice by using the projector determinant quantum Monte Carlo simulations combined with the method of local pinning fields. Long-range Néel orders are found for both the SU(4) and SU(6) cases at small and intermediate values of U. In both cases, the long-range Néel moments exhibit nonmonotonic behavior with respect to U, which first grow and then drop as U increases. This result is fundamentally different from the SU(2) case in which the Néel moments increase monotonically and saturate. In the SU(6) case, a transition to the columnar dimer phase is found in the strong interaction regime.

Dimerized solids and resonating plaquette order in SU(N)-Dirac fermions

We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.

Adiabatic loading of one-dimensional SU(N) alkaline-earth-atom fermions in optical lattices

Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.