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Frustration has proved to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model, where only the lowest-energy degrees of freedom are considered. In this paper we study a system corresponding to the strong trimerization limit of the spin 1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin 1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J>0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J>0 and J<0, a finite-temperature phase transition with a breaking of the discrete dihedral symmetry group D_6 of the model is present. For J<0, we find a transition temperature T^<_c/|J| = 1.566 +/- 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J>0 the transition occurs at an extremely low temperature, T^>_c ~= 0.0125 J. Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case., Comment: 18 pages including 18 figures and 1 table; replaced in order to match published version, most important change: added appendix with derivation of Hamiltonian from spin-1/2 Heisenberg model on trimerized kagome lattice

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbour exchange couplings on the kagome net, i.e. with coupling J in one lattice direction and couplings J' along the other two directions. For J/J' > 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground states: a ferrimagnetic state for J/J' < 1/2 and a large manifold of canted spin states for J/J' > 1/2. To include quantum effects self-consistently, we investigate the Sp(N) symmetric generalisation of the original SU(2) symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp(N) symmetric model depends on a parameter kappa that measures the importance of quantum effects. Our numerical calculations reveal that in the kappa-J/J' plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short- and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp(N) phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerised version of the original spin-1/2 model leads us to suggest that in the limit of strong anisotropy, J/J' >> 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition., Comment: 21 pages, 22 figures. Final version, PRB in press

We investigate the classical counterpart of an effective Hamiltonian for a strongly trimerized kagome lattice. Although the Hamiltonian only has a discrete symmetry, the classical groundstate manifold has a continuous global rotational symmetry. Two cases should be distinguished for the sign of the exchange constant. In one case, the groundstate has a 120^\circ spin structure. To determine the transition temperature, we perform Monte-Carlo simulations and measure specific heat, the order parameter as well as the associated Binder cumulant. In the other case, the classical groundstates are macroscopically degenerate. A thermal order-by-disorder mechanism is predicted to select another 120^\circ spin-structure. A finite but very small transition temperature is detected by Monte-Carlo simulations using the exchange method., Comment: 11 pages including 9 figures, uses IOP style files; to appear in J. Phys.: Condensed Matter (proceedings of HFM2006)

In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies [Hiroi et al.,2001]. It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the Sp(N) symmetric generalisation of this model in the large N limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase, incommensurate phases with and without long range order and a decoupled chain phase emerges., Comment: 6 pages, 6 figures, proceedings of the HFM2006 conference, to appear in a special issue of J. Phys.: Condens. Matter

We study low temperature properties of atomic gases in trimerized optical kagom\'{e} lattices. The laser arrangements that can be used to create these lattices are briefly described. We also present explicit results for the coupling constants of the generalized Hubbard models that can be realized in such lattices. In the case of a single component Bose gas the existence of a Mott insulator phase with fractional numbers of particles per trimer is verified in a mean field approach. The main emphasis of the paper is on an atomic spinless interacting Fermi gas in the trimerized kagom\'{e} lattice with two fermions per site. This system is shown to be described by a quantum spin 1/2 model on the triangular lattice with couplings that depend on the bond directions. We investigate this model by means of exact diagonalization. Our key finding is that the system exhibits non-standard properties of a quantum spin-liquid crystal: it combines planar antiferromagnetic order in the ground state with an exceptionally large number of low energy excitations. The possibilities of experimental verification of our theoretical results are critically discussed., Comment: 19 pages/14 figures, version to appear in Phys. Rev. A., numerous minor corrections with respect to former lanl submission

We study low temperature properties of an atomic spinless interacting Fermi gas in the trimerized Kagom\'e lattice for the case of two fermions per trimer. The system is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on bonds directions. Using exact diagonalizations we show that the system exhibits non-standard properties of a {\it quantum spin-liquid crystal}, combining a planar antiferromagnetic order with an exceptionally large number of low energy excitations., Comment: 4 pages & 4 figures + 2 tables, better version of Fig. 2

We demonstrate the possibility of creating and controlling an ideal and \textit{trimerized} optical Kagom\'e lattice, and study the low temperature physics of various atomic gases in such lattices. In the trimerized Kagom\'e lattice, a Bose gas exhibits a Mott transition with fractional filling factors, whereas a spinless interacting Fermi gas at 2/3 filling behaves as a quantum magnet on a triangular lattice. Finally, a Fermi-Fermi mixture at half filling for both components represents a frustrated quantum antiferromagnet with a resonating-valence-bond ground state and quantum spin liquid behavior dominated by continuous spectrum of singlet and triplet excitations. We discuss the method of preparing and observing such quantum spin liquid employing molecular Bose condensates., Comment: 4 pages, 1 figure. Missing affiliations added

The quasi-particle weight of a single hole in an antiferromagnetic background is studied in the semiclassical approximation. We start from the t-J model, generalize it to arbitrary spin S by employing an appropriate coherent state representation for the hole, and derive an effective action for the dynamics in the long-wavelength low-energy limit. In the same limit, we find an expression for the single-hole Green's function which we evaluate in an 1/S expansion. Our approach has the advantage of being applicable in one and in two dimensions. We find two qualitatively different results in these two cases: while in one dimension our results are compatible with a vanishing quasi-particle weight, this weight is found to be finite in two dimensions, indicating normal quasi-particle behavior of the hole in this last case., Comment: 9 pages, 1 figure

We study the collective diffusion in chain structures on anisotropic substrates like (112) bcc and (110) fcc surfaces with deep troughs in the substrate potential corrugation. These chain structures are aligned normal to the troughs and can move only along the troughs. In a combination of theoretical arguments and of numerical simulations, we study the mass transport in these anisotropic systems. We find that a mechanism similar to soliton diffusion, instead of single particle diffusion, is still effective at temperatures well above the melting temperature of the ordered chain structures. This mechanism is directly correlated with the ordered phases that appear at much lower temperatures. As a consequence, also the influence of frozen disorder is still visible above the melting temperature. Theoretically we predict a strong dependence of the pre-exponential factor and weak dependence of the activation energy on the concentration of frozen surface defects. These predictions are confirmed by the simulations., Comment: Latex file, 18 pages and 9 eps figures included

The first order phase transitions between a two-dimensional (2d) gas and the 2d solid of the first monolayer have been studied for the noble gases Ar, Kr and Xe on a NaCl(100) surface in quasi-equilibrium with the three-dimensional gas phase. Using linear temperature ramps, we show that the widths of the hysteresis loops of these transitions as a function of the heating rate, r, scales with a power law r^alpha with alpha between 0.4 and 0.5 depending on the system. The hysteresis loops for different heating rates are similar. The island area of the condensed layer was found to grow initially with a t^4 time dependence. These results are in agreement with theory, which predicts alpha = 0.5 and hysteresis loop similarity., Comment: 4 pages, 5 figures, Revtex

A coherent state representation for the electrons of ordered antiferromagnets is used to derive effective Hamiltonians for the dynamics of holes in such systems. By an appropriate choice of these states, the constraint of forbidden double occupancy can be implemented rigorously. Using these coherent states, one arrives at a path integral representation of the partition function of the systems, from which the effective Hamiltonians can be read off. We apply this method to the t-J model on the square lattice and on the triangular lattice. In the former case, we reproduce the well-known fermion-boson Hamiltonian for a hole in a collinear antiferromagnet. We demonstrate that our method also works for non-collinear antiferromagnets by calculating the spectrum of a hole in the triangular antiferromagnet in the self-consistent Born approximation and by comparing it with numerically exact results., Comment: 9 pages, Latex, 6 figures

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagom\'e lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of N\'eel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic ($\Delta S=1$) excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic ($\Delta S=0$) excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagom\'e lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets., Comment: 8 pages including 3 eps-figures, using epsfig package

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $\xi$, the susceptibility at the ordering wavevector $\chi(\bf Q)$, and the spin stiffness $\rho$ clearly reflects the existence of two temperature regimes -- a high temperature regime $T > T_{th}$, in which the disordering effect of vortices is dominant, and a low temperature regime $T < T_{th}$, where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For $T > T_{th}$, a satisfactory fit of the data is achieved, if the temperature dependence of $\xi$ and $\chi(\bf Q)$ is assumed to be of the form predicted by the Kosterlitz--Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around $T_{th} \simeq 0.28$., Comment: 13 pages, 8 Postscript figures

We study the topological defects in the classical Heisenberg antiferromagnet in two dimensions on a triangular lattice (HAFT). While the topological analysis of the order parameter space indicates that the defects are of $Z_2$ type, consideration of the energy leads us to a description of the low--energy stationary points of the action in terms of $\pm$ vortices, as in the planar XY model. Starting with the continuum description of the HAFT, we show analytically that its partition function can be reduced to that of a 2--dimensional Coulomb gas with logarithmic interaction. Thus, at low temperatures, the correlation length is determined by the spinwaves, while at higher temperatures we expect a crossover to a Kosterlitz--Thouless type behaviour. The results of recent Monte Carlo calculations of the correlation length are consistent with such a crossover., Comment: 9 pages, revtex, preprint: ITP-UH 03/94

We investigate the phase diagram and the critical properties of the adsorbate system sulphur/ruthenium(0001) in the coverage region $\frac{1}{4} < \Theta < \frac{1}{3}$ by means of Monte-Carlo simulations of a simple lattice gas model on a triangular lattice. The model contains only repulsive nearest and next-nearest neighbor interactions. Combining results obtained by using both Glauber and Kawasaki kinetics in the simulations we identify two tricritical points, three coexistence regions and a eutectic point in the phase diagram of the system. Our results agree with the findings of recent experimental work on S/Ru(0001). Furthermore we are able to add certain details to the experimentally observed phase diagram., Comment: 15 pages (incl. 8 Postscript figures), LaTeX, ITP-UH 21/93

We study the ground state properties of the S=$\frac{1}{2}$ Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour ($J$) and next-nearest neighbour ($\alpha J$) couplings. Classically, this system is known to be ordered in a $120^\circ$ N\'eel type state for values $-\infty<\alpha\le 1/8$ of the ratio $\alpha$ of these couplings and in a collinear state for $1/8<\alpha<1$. The order parameter ${\cal M}$ and the helicity $\chi$ of the $120^\circ$ structure are obtained by numerical diagonalisation of finite periodic systems of up to $N=30$ sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region $-\infty<\alpha< 1/8$. It appears that the SW theory is still valid for the simple triangular HAF ($\alpha=0$) although the sublattice magnetisation ${\cal M}$ is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameter ${\cal N}$ of the collinear order support the previous conjecture of a first order transition between the $120^\circ$ and the collinear order at $\alpha \simeq 1/8$., Comment: 27 pages, LaTeX, figures on request, ITP-UH-19/93