Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite

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 pres

Atomic quantum gases in Kagom\'e lattices

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 adde

Finite-temperature ordering in a two-dimensional highly frustrated spin model

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

The Heisenberg antiferromagnet on a triangular lattice: topological excitations

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 03/9

Atomic Fermi gas in the trimerized Kagom\'e lattice at the filling 2/3

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.

Scaling of the Hysteresis Loop in Two-dimensional Solidification

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, Revte

Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice

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 lattic

Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

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 figure