We propose an experimentally feasible setup with ultracold alkaline earth atoms to simulate the dynamics of U(1) lattice gauge theories in 2+1 dimensions with a Chern-Simons term. To this end we consider the ground state properties of spin-5/2 alkaline earth fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin liquid state with 2π/3 flux per plaquette, which spontaneously violates time reversal invariance. We demonstrate that due to the breaking of time reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge field dynamics. We discuss also properties of the lowest energy competing orders.One of the main motivations of studying ultracold atoms in optical lattices is the high extent of experimental control. Such systems are very flexible and therefore are good candidates for simulating other quantum systems, where experimental control is more cumbersome. There is a vast number of proposals where ultracold quantum gases can serve as simulators of condensed matter, or even high energy physics systems (see for instance Ref. [1]). An important example of such proposals concerns the recent experimental realization of trapping and cooling of ultracold alkaline earth atoms [2][3][4], which could serve for quantum simulators of high symmetry magnetism [5]. Despite of these spectacular developments, one of the most important goals of quantum simulators remains still to be realized, namely the simulation of quantum gauge theories, which appear first of all in high energy physics, but arise naturally also in many areas of condensed matter physics, such as physics of frustrated systems, or of high temperature superconductors [6]. The main difficulty here is to map the many modes of the gauge field to those of an atomic ensemble. Very recent proposals use mixtures of fermionic and bosonic atoms, so that the bosons are the mediators of the gauge field [7,8].Here we propose another, somewhat simpler, scheme with only a single species of ultracold atoms to simulate a 2+1 dimensional U(1) lattice gauge theory with a Chern-Simons term. Our proposal is based on the observation that low energy excitations of certain Mott insulators can be described by lattice gauge theories [6,9]. The Mott insulator we consider here is formed by spin-5/2 alkaline earth atoms, such as 173 Yb, which, as was shown by Hermele et al.[10], can exhibit time reversal symmetry breaking, and have a so called chiral spin liquid (CSL) ground state in a square lattice. CSL states lack any kind of long range order, but due to the violation of time reversal invariance, they are stable also at low temperatures. The fluctuations above the CSL state are described by a U(1) gauge theory with a Chern-Simons term arising from the chiral (time reversal symmetry breaking) nature of the ground state [11]. Here we treat the case of ...

The one-dimensional SU(n) Hubbard model is investigated numerically for n = 2, 3, 4, and 5 at half filling and 1/n filling using the density-matrix renormalization-group (DMRG) method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive U if n > 2. Furthermore, it is shown that the transition to the gapped phase at Uc = 0 is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd n. In the 1/n-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for U > Uc = 0, the spin sector remains gapless, and the ground state is non-dimerized.

The one-dimensional repulsive SU(n) Hubbard model is investigated analytically by bosonization approach and numerically using the density-matrix renormalization-group (DMRG) method for n = 3, 4, and 5 for commensurate fillings f = p/q where p and q are relatively prime. It is shown that the behavior of the system is drastically different depending on whether q > n, q = n, or q < n. When q > n, the umklapp processes are irrelevant, the model is equivalent to an n-component Luttinger liquid with central charge c = n. When q = n, the charge and spin modes are decoupled, the umklapp processes open a charge gap for finite U > 0, whereas the spin modes remain gapless and the central charge c = n − 1. The translational symmetry is not broken in the ground state for any n. On the other hand, when q < n, the charge and spin modes are coupled, the umklapp processes open gaps in all excitation branches, and a spatially nonuniform ground state develops. Bond-ordered dimerized, trimerized or tetramerized phases are found depending on the filling.

We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin F > 1/2, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low energy effective models with nearest-neighbor interactions, and their properties. We apply our method to F = 3/2, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for F = 3/2 fermions that the plaquette state appearing in the highly symmetric SU(4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU(2) flux state, that is always suppressed for repulsive interactions in absence of external magnetic field. The SU(2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For F = 5/2 fermions a similar SU(2) plaquette phase is found to be the ground state without external magnetic field.