Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the “kagome-ice” problem. We discuss the similarity and dissimilarity of the magnetization curves of the “kagome-ice” state and the two-dimensional kagome lattice.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

Orbital order in Mott insulators of spinless p-band fermions

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.     

Magnetic properties of <Superscript>3</Superscript>He on the recursive lattices

We considered the Heisenberg model on the recursive lattices with multi-spin interaction in a strong magnetic field as an approximation of the two-dimensional kagome lattice, as well as hexagonal recursive lattices as an approximation of triangular lattice, for solid ³He. In a strong magnetic field it is possible to approximate the Heisenberg model with the Izing one. Using dynamic approach, we obtain exact recursion relations for partition functions. Diagrams of the magnetization versus external magnetic field with different spin-exchange parameters and temperatures are presented. Magnetization plateaux, bifurcation points, and doublings are obtained.     

Observation of vortex pinning in Bose-Einstein condensates

We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates. Vortices are pinned to columnar pinning sites created by a corotating optical lattice superimposed on the rotating Bose-Einstein condensates. We study the effects of two types of optical lattice: triangular and square. In both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural crossover in the vortex lattice.     

Orbital ordering and frustration of p-band Mott insulators

We investigate the general structure of orbital exchange physics in Mott-insulating states of p-orbital systems in optical lattices. Orbital orders occur in both the triangular and kagome lattices. In contrast, orbital exchange in the honeycomb lattice is frustrated as described by a novel quantum 120 degrees model. Its classical ground states are mapped into configurations of the fully packed loop model with an extra U(1) rotation degree of freedom. Quantum orbital fluctuations select a six-site plaquette ground state ordering pattern in the semiclassical limit from the "order from disorder" mechanism. This effect arises from the appearance of a zero energy flat band of orbital excitations.     

Vortex lattice transitions in cyclic spinor condensates

We study the energetics of vortices and vortex lattices produced by rotation in the cyclic phase of F=2 spinor condensates. In addition to the familiar triangular lattice predicted by Tkachenko for 4He, many more complex lattices appear in this system as a result of the spin degree of freedom. In particular, we predict a magnetic-field-driven transition from a triangular lattice to a honeycomb lattice. Other transitions and lattice geometries are driven at constant field by changes in the temperature-dependent ratio of charge and spin stiffnesses, including a transition through an aperiodic vortex structure. Finally, we compute the renormalization of the ratio of the spin and charge stiffnesses from thermal fluctuations using a nonlinear sigma model analysis.     

Designing isotropic interactions for self-assembly of complex lattices

We present a direct method for solving the inverse problem of designing isotropic potentials that cause self-assembly into target lattices. Each potential is constructed by matching its energy spectrum to the reciprocal representation of the lattice to guarantee that the desired structure is a ground state. We use the method to self-assemble complex lattices not previously achieved with isotropic potentials, such as a snub square tiling and the kagome lattice. The latter is especially interesting because it provides the crucial geometric frustration in several proposed spin liquids.     

Exact entropy of dimer coverings for a class of lattices in three or more dimensions

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the method also works for graphs without translational symmetry. The partition function for dimer coverings on these lattices can be determined also for a class of assignments of different activities to different edges.     

Hard-core bosons on the kagome lattice: valence-bond solids and their quantum melting

Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.     

Reversible random sequential adsorption of dimers on a triangular lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca2+ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.     

Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices

We study numerically the nature of the diffusion process on a honeycomb and a quasi-lattice, where a point particle, moving along the bonds of the lattice, scatters from randomly placed scatterers on the lattice sites according to strictly deterministic rules. For the honeycomb lattice fully occupied by fixed rotators two (symmetric) isolated critical points appear to be present, with the same hyperscaling relation as for the square and the triangular lattices. No such points appear to exist for the quasi-lattice. A comprehensive comparison is made with the behavior on the previously studied square and triangular lattices. A great variety of diffusive behavior is found, ranging from propagation, superdiffusion, normal, quasi-normal, and anomalous, to absence of diffusion. The influence of the scattering rules as well as of the lattice structure on the diffusive behavior of a point particle moving on the all lattices studied so far is summarized.     

Spin phonon induced collinear order and magnetization plateaus in triangular and kagome antiferromagnets: applications to CuFeO2

We study the effect of spin-lattice coupling on triangular and kagome antiferromagnets and find that even moderate couplings can induce complex collinear orders. On coupling classical Heisenberg spins on the triangular lattice to Einstein phonons, a rich variety of phases emerge including the experimentally observed four sublattice state and the five sublattice 1/5th plateau state seen in the magnetoelectric material CuFeO(2). Also, we predict magnetization plateaus at 1/3, 3/7, 1/2, 3/5, and 5/7 at these couplings. Strong spin-lattice couplings induce a striped collinear state, seen in alpha-NaFeO(2) and MnBr(2). On the kagome lattice, moderate spin-lattice couplings induce collinear order, but an extensive degeneracy remains.     

Quantum dimer model on the kagome lattice: solvable dimer-liquid and ising gauge theory

We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices include the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Using geometrical properties of the lattice, several results are obtained exactly, including the full spectrum of a dimer liquid. These models offer a very natural-and maybe the simplest possible-framework to illustrate general concepts such as fractionalization, topological order, and relation to Z2 gauge theories.     

Isolated structures in two-dimensional optical superlattice

Overlaying commensurate optical lattices with various configurations called superlattices can lead to exotic lattice topologies and, in turn, a discovery of novel physics. In this study, by overlapping the maxima of lattices, a new isolated structure is created, while the interference of minima can generate various “sublattice” patterns. Three different kinds of primitive lattices are used to demonstrate isolated square, triangular, and hexagonal “sublattice” structures in a two-dimensional optical superlattice, the patterns of which can be manipulated dynamically by tuning the polarization, frequency, and intensity of laser beams. In addition, we propose the method of altering the relative phase to adjust the tunneling amplitudes in “sublattices”. Our configurations provide unique opportunities to study particle entanglement in “lattices” formed by intersecting wells and to implement special quantum logic gates in exotic lattice geometries.     

Nested cluster algorithm for frustrated quantum antiferromagnets

Frustrated antiferromagnets are important materials whose quantum Monte Carlo simulation suffers from a severe sign problem. We construct a nested cluster algorithm which uses a powerful strategy to address this problem. For the spin 1/2 Heisenberg antiferromagnet on a kagome and on a frustrated square lattice the sign problem is eliminated for large systems. The method is applicable to general lattice geometries but limited to moderate temperatures.     

Breakdown of universality in directed spiral percolation

Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated in this model are generally rarefied and have chiral dangling ends on both the square and triangular lattices. It is found that the clusters are more compact and less anisotropic on the triangular lattice than on the square lattice. The elongation of the clusters is in a different direction than the imposed directional constraint on both the lattices. The values of some of the critical exponents and fractal dimension are found considerably different on the two lattices. The DSP model then exhibits a breakdown of universality in 2D between the square and triangular lattices. The values of the critical exponents obtained for the triangular lattice are not only different from that of the square lattice but also different form other percolation models.Received: 12 March 2004, Published online: 23 July 2004PACS: 02.50.-r Probability theory, stochastic processes, and statistics - 64.60.-i General studies of phase transitions - 72.80.Tm Composite materials     

Degenerate ferrimagnetic ground state of frustrated kagome lattice

The frustrated Ising model on kagome lattice with nearest-neighboring antiferromagnetic interaction is investigated by using Monte Carlo simulation of the Wang-Landau algorithm and Glauber dynamics. The geometrical frustration leads to a particularly high degeneracy of ground states in this system. A small magnetic field applied can lift the degeneracy partially, and produce the magnetization plateau of 1/3 saturate value (Ms), which is analogous to the magnetic behavior in triangular antiferromagnetic system. However, different from the long-range ferrimagnetic state responsible for 1/3 Ms plateau in triangular lattice, the ferrimagnetic ground state corresponding to 1/3 Ms plateau in kagome lattice is short-ranged and still highly degenerate. Furthermore, the spin configuration of these degenerate ferrimagnetic ground states show an inherent characteristic that the spins along the magnetic field must be aligned on the closed loops, which can be well understood in terms of geometrical frustration.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Kinetic ferromagnetism on a kagome lattice

We study strongly correlated electrons on a kagome lattice at 1/6 (and 5/6) filling. They are described by an extended Hubbard Hamiltonian. We are concerned with the limit |t|相似文献