Lattice to boat house, Cleveland Point House, Cleveland

Lattice behind pull-down blind to boat house.

Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants

We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular lattices, using high-temperature series expansions. We consider a model with two exchange constants J1 and J2 on a lattice that interpolates between the limits of a square lattice (J1=0), a triangular lattice (J2=J1), and decoupled linear chains (J2=0). In all cases, the susceptibility, which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature Tp. Scaling the exchange constants to get the same peak temperature shows that the susceptibilities for the square lattice and linear chain limits have similar magnitudes near the peak. Maximum deviation arises near the triangular-lattice limit, where frustration leads to much smaller susceptibility and with a flatter temperature dependence. We compare our results to the inorganic materials Cs2CuCl4 and Cs2CuBr4 and to a number of organic molecular crystals. We find that the former (Cs2CuCl4 and Cs2CuBr4) are weakly frustrated and their exchange parameters determined through the temperature dependence of the susceptibility are in agreement with neutron-scattering measurements. In contrast, the organic materials considered are strongly frustrated with exchange parameters near the isotropic triangular-lattice limit.

Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground-state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave (LSW) theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)(2)X family of superconducting molecular crystals. The ground-state energy, the staggered magnetization, magnon excitation spectra, and spin-wave velocities are computed as functions of the ratio of the antiferromagnetic exchange between the second and first neighbours, J(2)/J(1). We find that near J(2)/J(1) = 0.5, i.e., in the region where the classical spin configuration changes from a Neel-ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. in this region, the quantum correction to the magnetization is large but finite. This is in contrast to the case for the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J(2)/J(1), the model becomes a set of chains with frustrated interchain coupling. For J(2) > 4J(1), the quantum correction to the magnetization, within LSW theory, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, the quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustrated interchain coupling.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Free energy approximations in simple lattice proteins

This work addresses the question of whether it is possible to define simple pairwise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how reliable it could possibly be. In a two-dimensional, infinite lattice model system one can calculate exact free energies by exhaustive enumeration. A series of approximations were fitted to exact results to assess the feasibility and utility of pairwise free energy terms. Approximating the true free energy with pairwise interactions gives a poor fit with little transferability between systems of different size. Adding extra artificial terms to the approximation yields better fits, but does not improve the ability to generalize from one system size to another. Furthermore, one cannot distinguish folding from nonfolding sequences via the approximated free energies. Most usefully, the methodology shows how one can assess the utility of various terms in lattice protein/polymer models. (C) 2001 American Institute of Physics.

Ladder operators for integrable one-dimensional lattice models

A generalised ladder operator is used to construct the conserved operators for any one-dimensional lattice model derived from the Yang-Baxter equation. As an example, the low order conserved operators for the XYh model are calculated explicitly.

Drinfield twists and alegebraic Bethe ansatz of the supersymmetric t-J model

We construct the Drinfeld twists (factorizing F-matrices) for the supersymmetric t-J model. Working in the basis provided by the F-matrix (i.e. the so-called F-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the gl(2\1) invariant t-J model.

Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

We construct the Drinfeld twists ( factorizing F-matrices) of the gl(m-n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix ( the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m-n) supersymmetric model.

Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice

Motivated by the unconventional properties and rich phase diagram of NaxCoO2 we consider the electronic and magnetic properties of a two-dimensional Hubbard model on an isotropic triangular lattice doped with electrons away from half-filling. Dynamical mean-field theory (DMFT) calculations predict that for negative intersite hopping amplitudes (t < 0) and an on-site Coulomb repulsion, U, comparable to the bandwidth, the system displays properties typical of a weakly correlated metal. In contrast, for t > 0 a large enhancement of the effective mass, itinerant ferromagnetism, and a metallic phase with a Curie-Weiss magnetic susceptibility are found in a broad electron doping range. The different behavior encountered is a consequence of the larger noninteracting density of states (DOS) at the Fermi level for t > 0 than for t < 0, which effectively enhances the mass and the scattering amplitude of the quasiparticles. The shape of the DOS is crucial for the occurrence of ferromagnetism as for t > 0 the energy cost of polarizing the system is much smaller than for t < 0. Our observation of Nagaoka ferromagnetism is consistent with the A-type antiferromagnetism (i.e., ferromagnetic layers stacked antiferromagnetically) observed in neutron scattering experiments on NaxCoO2. The transport and magnetic properties measured in NaxCoO2 are consistent with DMFT predictions of a metal close to the Mott insulator and we discuss the role of Na ordering in driving the system towards the Mott transition. We propose that the Curie-Weiss metal phase observed in NaxCoO2 is a consequence of the crossover from a bad metal with incoherent quasiparticles at temperatures T > T-* and Fermi liquid behavior with enhanced parameters below T-*, where T-* is a low energy coherence scale induced by strong local Coulomb electron correlations. Our analysis also shows that the one band Hubbard model on a triangular lattice is not enough to describe the unusual properties of NaxCoO2 and is used to identify the simplest relevant model that captures the essential physics in NaxCoO2. We propose a model which allows for the Na ordering phenomena observed in the system which, we propose, drives the system close to the Mott insulating phase even at large dopings.

Lattice-dome design using a knowledge-based system approach

In the design of lattice domes, design engineers need expertise in areas such as configuration processing, nonlinear analysis, and optimization. These are extensive numerical, iterative, and lime-consuming processes that are prone to error without an integrated design tool. This article presents the application of a knowledge-based system in solving lattice-dome design problems. An operational prototype knowledge-based system, LADOME, has been developed by employing the combined knowledge representation approach, which uses rules, procedural methods, and an object-oriented blackboard concept. The system's objective is to assist engineers in lattice-dome design by integrating all design tasks into a single computer-aided environment with implementation of the knowledge-based system approach. For system verification, results from design examples are presented.