Interplay of spin and lattice degrees of freedom in the frustrated antiferromagnet CdCr2O4: High-field and temperature-induced anomalies of the elastic constants

Temperature and magnetic field studies of the elastic constants of the chromium spinel CdCr2O4 show pronounced anomalies related to strong spin-phonon coupling in this frustrated antiferromagnet. A detailed comparison of the longitudinal acoustic mode propagating along the 111] direction with a theory based on an exchange-striction mechanism leads to an estimate of the strength of the magnetoelastic interaction. The derived spin-phonon coupling constant is in good agreement with previous determinations based on infrared absorption. Further insight is gained from intermediate and high magnetic field experiments in the field regime of the magnetization plateau. The role of the antisymmetric Dzyaloshinskii-Moriya interaction is discussed.

Lattice dynamics of hexagonal ice

The lattice dynamics of hexagonal ice is worked out with the force constants deduced from the experimental elastic constants.

Lattice vibrations and specific heat of zinc blende

The dispersion relations, frequency distribution function and specific heat of zinc blende have been calculated using Houston's method on (1) A short range force (S. R.) model of the type employed in diamond by Smith and (2) A long range model assuming an effective charge Ze on the ions. Since the elastic constant data on ZnS are not in agreement with one another the following values were used in these calculations: {Mathematical expression}. As compared to the results on the S. R. model, the Coulomb force causes 1. A splitting of the optical branches at (000) and a larger dispersion of these branches; 2. A rise in the acoustic frequency branches the effect being predominant in a transverse acoustic branch along [110]; 3. A bridging of the gap of forbidden frequencies in the S. R. model; 4. A reduction of the moments of the frequency distribution function and 5. A flattening of the Θ- T curve. By plotting (Θ/Θ0) vs. T., the experimental data of Martin and Clusius and Harteck are found to be in perfect coincidence with the curve for the short range model. The values of the elastic constants deduced from the ratio Θ0 (Theor)/Θ0 (Expt) agree with those of Prince and Wooster. This is surprising as several lines of evidence indicate that the bond in zinc blende is partly covalent and partly ionic. The conclusion is inescapable that the effective charge in ZnS is a function of the wave vector {Mathematical expression}.

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Search on a hypercubic lattice using a quantum random walk. II. d = 2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d = 2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article A. Patel and M. A. Rahaman, Phys. Rev. A 82, 032330 (2010)] provides an O(root N ln N) algorithm, which is not optimal. The scaling behavior can be improved to O(root N ln N) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78, 012310 (2008)]. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

Search on a Hypercubic Lattice using Quantum Random Walk

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d=2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article [ A. Patel and M. A. Rahaman Phys. Rev. A 82 032330 (2010)] provides an O(√NlnN) algorithm, which is not optimal. The scaling behavior can be improved to O(√NlnN) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78 012310 (2008). We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

Mechanisms underlying two kinds of surface effects on elastic constants

ABSTRACT Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample: elastic modulus either decreases or increases with decreas- ing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the mi- crostructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, resulting in the decrease of the elastic moduli with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coor- dination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair po- tential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface re- spectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one- dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.

A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

LDA or GGA? A combined experimental inelastic neutron scattering and ab initio lattice dynamics study of alkali metal hydrides

In a previous work, we carried out inelastic neutron scattering (INS) spectroscopy experiments and preliminary first principles calculations on alkali metal hydrides. The complete series of alkali metal hydrides, LiH, NaH, KH, RbH and CsH was measured in the high-resolution TOSCA INS spectrometer at ISIS. Here, we present the results of ab initio electronic structure calculations of the properties of the alkali metal hydrides using both the local density approximation (LDA) and the generalized gradient approximation (GGA), using the Perdew–Burke–Ernzerhof (PBE) parameterization. Properties calculated were lattice parameters, bulk moduli, dielectric constants, effective charges, electronic densities and inelastic neutron scattering (INS) spectra. We took advantage of the currently available computer power to use full lattice dynamics theory to calculate thermodynamic properties for these materials. For the alkali metal hydrides (LiH, NaH, KH, RbH and CsH) using lattice dynamics, we found that the INS spectra calculated using LDA agreed better with the experimental data than the spectra calculated using GGA. Both zero-point effects and thermal contributions to free energies had an important effect on INS and several thermodynamic properties.

Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model

We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the lightquark masses, the form factor f+(0), arising in semileptonic K → π transition at zero momentum transfer, as well as the decay-constant ratio fK / fπ of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)L × SU(2)R and SU(3)L×SU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant αs.