Density matrix renormalization group algorithm for Bethe lattices of spin-1/2 or spin-1 sites with Heisenberg antiferromagnetic exchange

A density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity Z = 3 and antiferromagnetic exchange between nearest-neighbor spins s = 1/2 or 1 sites in successive generations g. The algorithm is accurate for s = 1 sites. The ground states are magnetic with spin S(g) = 2(g)s, staggered magnetization that persists for large g > 20, and short-range spin correlation functions that decrease exponentially. A finite energy gap to S > S(g) leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for s = 1/2 and 1 are interpreted in terms of an analytical three-site model.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Orientational relaxation in a random dipolar lattice: Wave-number and frequency dependence

In order to understand the role of translational modes in the orientational relaxation in dense dipolar liquids, we have carried out a computer ''experiment'' where a random dipolar lattice was generated by quenching only the translational motion of the molecules of an equilibrated dipolar liquid. The lattice so generated was orientationally disordered and positionally random. The detailed study of orientational relaxation in this random dipolar lattice revealed interesting differences from those of the corresponding dipolar liquid. In particular, we found that the relaxation of the collective orientational correlation functions at the intermediate wave numbers was markedly slower at the long times for the random lattice than that of the liquid. This verified the important role of the translational modes in this regime, as predicted recently by the molecular theories. The single-particle orientational correlation functions of the random lattice also decayed significantly slowly at long times, compared to those of the dipolar liquid.

Proton spin lattice relaxation in lithium ammonium sulphate LiNH4SO4

Lithium ammonium sulphate (LAS) undergoes a phase transition at TC1=459.5K from a paraelectric phase (phase I) to a ferroelectric phase (phase II) and again at TC2=283K to a polar ferroelastic phase (phase III). Proton spin lattice relaxation time measured at 10 MHz in powdered LAS in the temperature range 480 to 77K shows discontinuous changes at the two transitions.

Mean-field results of a lattice-gas model of multilayer adsorption

A lattice-gas model of multilayer adsorption has been solved in the mean-field approximation by a different numerical method. Earlier workers obtained a single solution for all values of temperature and pressure. In the present work, multiple solutions have been obtained in certain regions of temperature and pressure which give rise to bysteresis in the adsorption isotherm. In addition, we have obtained a parameter which behaves like an order parameter for the transition. The potential-energy function shows a double minimum in the region of bysteresis and a single maximum elsewhere.

On states, on a lattice, with half-integral charge

In certain molecular models, and related one-dimensional field theories, localized objects appear with half-integral expectation values of charge. We consider whether these states are eigenstates of charge, with half-integral eigenvalue. We find that it is indeed so for a suitably diffuse definition of the charge operator in question. This diffuse charge operator has a spectrum which approaches a continuum. The analysis is made on a lattice, to avoid divergence ambiguities, and on a finite length, which is only subsequently made large. The half-integral charge phenomenon is not tied to solitons, but can also arise as an end effect.

Proline ring conformations corresponding to a bistable jump model from 13C spin-lattice relaxation times

A formalism for extracting the conformations of a proline ring based on the bistable jump model of R. E. London [(1978) J. Am. Chem. Soc. 100, 2678-2685] from 13C spin-lattice relaxation times (T1) is given. The method is such that the relaxation data are only partially used to generate the conformations; these conformations are constrained to satisfy the rest of the relaxation data and to yield acceptable ring geometry. An alternate equation for T1 of 13C nuclei to that of London is given. The formalism is illustrated through an example.

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Size effect on the lattice parameter of KCl during mechanical milling

The size effect on the lattice parameter of ionic KCl nanocrystals was studied systematically during mechanical milling of Pure KCl powder under vacuum. The results suggest anomalous lattice expansion, with the lattice parameter increasing from 6.278 angstrom at d = 6 mu m to 6.30307 angstrom at d = 85 mn. The defects generated during ball milling of KCl and surface stress are deemed to be responsible for this lattice parameter expansion. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Proton Spin-Lattice Relaxation in Sodium Ammonium Selenate Dihydrate:NaNHaSeOa.2He0

Proton spin-lattice relaxation studies in sodium ammonium selenate dihydrate carried out in the temperature range 130 to 300 K at 10 MHz show a continuous change in T, at T, indicating a second order phase transition. This compound is a typical case of a highly hindered solid wherein the thermally activated reorientations of ammonium ions freeze well above 77 K, as seen by NMR.Untersuchimgen der Protonen-Spin-Gitter-Relaxation in Natriuni-Ammoniumselenat-Dihydrat bei 10 MHz im Temperaturbereich 130 bis 300 K zeigen eine kontinuierliche Andernng in TI bei T, und ergeben einen Phasenubergang zweiter Art. Diese Verbindung ist ein typischer Fall eines stark ,,behinderten" Festkarpers, in dein die thermisch aktivierten Reorientierungen der Ammoniumionen weit oberhalb 77 H einfrieren, wie die NMR-Ergebnisse zeigen.

Pyrrolidine ring conformations in prolyl peptides from 13C spin-lattice relaxation times

A method was developed in the framework of a bistable jump model to obtain the pyrrolidine ring conformations in proline peptides from 13C spin-lattice relaxation times. Equations are presented expressing the ring torsions in terms of the 13C spin-lattice relaxation times of the ring carbons. This method was applied to 26 pyrrolidine ring systems and acceptable conformations were obtained.

Large Low-Frequency Fluctuations in the Velocity of a Driven Vortex Lattice in a Single Crystal of 2H-NbSe2 Superconductor

The driven state of a well-ordered flux line lattice in a single crystal of 2H-NbSe2 in the time domain has revealed the presence of substantial fluctuations in velocity, with large and distinct time periods (similar to seconds). A superposition of a periodic drive in the driven vortex lattice causes distinct changes in these fluctuations. We propose that prior to the onset of the peak effect there exists a heretofore unexplored regime of coherent dynamics, with unexpected behavior in velocity fluctuations.

Origin of activation of Lattice Oxygen and Synergistic Interaction in Bimetal-Ionic Ce0.89Fe0.1Pd0.01O2-delta Catalyst

Flourite-type nanocrystalline Ce0.9Fe0.1O2-delta and Ce0.89Fe0.1Pd0.01O2-delta solid solutions have been synthesized by solution combustion method,'.which show higher oxygen storage/release property (OSC) compared to CeO2 and Ce0.8Zr0.2O2. Temperature programmed reduction an XPS study reveal that the presence of Pd ion in Ce0.9Fe0.1O2-delta facilitates complete reduction of Fe3+ to Fe2+ state and partial reduction of Ce4+ to Ce3+ state at.temperatures as low as 105 degrees C compared to 400 degrees C for monometal-ionic Ce0.9Fe0.1O2-delta. Fe3+ ion is reduced to Fe2+ and not to Feo due to favorable redox potential for Ce4+ + Fe2+ -> Ce3+ + Fe3+ reaction. Using first-principles density functional theory calculation we determine M-O (M = Pd, Fe, Ce) bond lengths, and find that bond lengths vary from shorter (2.16 angstrom) to longer (2.9 angstrom) bond distances compared to mean Ce-O bond distance of 2.34 angstrom. for CeO2. Using these results in bond valence analysis, we show that oxygen with bond valences as low as -1.55 are created, leading to activation of lattice oxygen in the bimetal ionic catalyst. Temperatures of CO oxidation and NO reduction by CO/H-2 are lower with the bimetalionic Ce0.89Fe0.1Pd0.01O2-delta catalyst compared to monometal-ionic Ce0.9Fe0.1O2-delta and Ce0.99Pd0.01O2-delta catalysts. From XPS studies of Pd impregnated on CeO2 and Fe2O3 oxides, we show that the synergism leading to low temperature activation of lattice oxygen in bimetal-ionic catalyst Ce0.89Fe0.1Pd0.01O2-delta is due to low-temperature reduction of Pd2+ to Pd-0, followed by Pd-0 + 2Fe(3+) -> Pd2+ + 2Fe(2+), Pd-0 + 2Ce(4+) -> Pd2+ + 2Ce(3+) redox reaction.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

Structural Investigation of Activated Lattice Oxygen in Ce1-xSnxO2 and Ce1-x-ySnxPdyO2-delta by EXAFS and DFT calculation

Substitution of Sn4+ ion in CeO2 creates activated oxygen in Ce0.8Sn0.2O2 leading to higher oxygen storage capacity compared to Ce0.8Zr0.2O2. With Pd ion substitution in Ce0.8Sn0.2O2,activation of oxygen is further enhanced as observed from the H-2/TPR study. Both EXAFS analysis and DFT calculation reveal that in the solid solution Ceexhibits 4 + 4 coordination, Sri exhibits 4 + 2 + 2 coordination and Pd has 4 + 3 coordination. While the oxygen in the First four coordination with short M-O bonds are strongly held in the lattice, the oxygens in the second and higher coordinations with long M-O bonds are weakly bound, and they are the activated oxygen ill the lattice. Bond valence analysis shows that oxygen with valencies as low its 1.65 are created by the Sn and Pd ion Substitution. Another interesting observation is that H-2/TPR experiment of Ce1-xSnxO2 shows a broad peak starting from 200 to 500 degrees C, while the same reduction is achieved in a single step at similar to 110 degrees C in presence Pd2+ on. Substitution of Pd2+ ion thus facilitates synergistic reduction of the catalyst at lower temperature. We have shown that simultaneous reduction of the Ce4+ and Sr4+ ions by Pd-0 is the synergistic interaction leading to high oxygen storage capacity at low temperature.