NNN Interactions Research Articles

Influence of NNN interaction and existence of breathers in a quasi-discrete Heisenberg helimagnetic spin system

In this work, we investigate the existence and properties of discrete bright and dark breathers in a one-dimensional Heisenberg helimagnet incorporating bilinear, helical, NNN and anisotropic interactions. The Hamiltonian is bosonized using the Dyson–Maleev transformation and the coherent state representation is selected as the fundamental representation of the system. With the help of multiple scales combined with quasi-discreteness approximation, the dynamical equation is reduced to a nonlinear Schrödinger equation (NLSE). By employing the solution of NLSE derived using inverse scattering technique (IST), the bright and dark type breather solutions are constructed. The effect of helicity and NNN interactions on these breather modes is also analysed.

Observation of delocalization transition in topological waveguide arrays with long-range interactions.

Topological edge states are a generic feature of topological insulators, and the long-range interactions, which break certain properties of topological edge states, are always non-negligible in real physical systems. In this Letter, we investigate the influence of next-nearest-neighbor (NNN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) model by extracting the survival probabilities at the boundary of the photonic lattices. By introducing a series of integrated photonic waveguide arrays with different strengths of long-range interactions, we experimentally observe delocalization transition of light in SSH lattices with nontrivial phase, which is in good agreement with our theoretical predictions. The results indicate that the NNN interactions can significantly affect the edge states, and that the localization of these states can be absent in topologically nontrivial phase. Our work provides an alternative way to investigate the interplay between long-range interactions and localized states, which may stimulate further interest in topological properties in relevant structures.

Effective two-body ΛN → NN weak potentials deduced from three-body ΛNN → NNN interactions and hypernuclear non-mesonic weak decay rates

Abstract We intend to study the role of the three-body weak ΛNN → NNN interaction in two-nucleon induced hypernuclear non-mesonic weak decay. The three-body weak interactions are constructed on the basis of the meson-pair exchange (MPE) model and then we derive the effective two-body ΛN → NN weak potentials from the three-body interactions based on the Loiseau–Nogami–Ross approximation. The strong coupling constants of MPE are taken from the Nijmegen ESC and GESC models and the weak ones of MPE are evaluated in the weak Λ–n mixing model by Dalitz and Von Hippel [Phys. Lett. 10, 153 (1964)]. The effective two-body ΛN → NN weak potentials are applied to evaluate hypernuclear non-mesonic decay rates, which should give a certain additional contribution to the two-nucleon induced decay rate Γ2N. Calculations of $\Gamma ^{({\text{eff.2B}})}_{nm}$ are done for $^5_\Lambda {\rm He}$, $^{11}_\Lambda {\rm B}$, and $^{12}_\Lambda {\rm C}$ and the results are compared with experimental data $\Gamma ^\mathrm{exp}_{2N}$. We have demonstrated the possibility of accounting for the two-nucleon induced non-mesonic decays of light and p-shell hypernuclei by introducing the effective two-body potentials deduced from the three-body weak interactions, though the calculated $\Gamma ^{(\text{eff.2B})}_{nm}$ still includes uncertainties. Discussions and limitations of our “effective two-body ΛN → NN model” are given.

Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with next-to-nearest-neighbor interactions

We suggest a method for fast and robust quantum-state transfer in a Su-Schrieffer-Heeger (SSH) chain, which exploits the use of next-to-nearest-neighbour (NNN) interactions. The proposed quantum protocol combines a rapid change in one of the topological edge states, induced by a modulation of nearest-neighbour interactions, with a fine tuning of NNN interactions operating a counter-adiabatic driving. The latter cancels nonadiabatic excitations from the edge state multiplicity to the energy bands. We use this shortcut technique for topological pumping of edge states on a single dimerized chain and also through an interface that connects two dimerized Su-Schrieffer-Heeger chains with different topological order. We investigate the robustness of this protocol against both uncorrelated and correlated disorder, and demonstrate its strong resilience to the former in comparison to traditional adiabatic protocols for topological chains. We show that introducing spatial correlations in the disorder increases the robustness of the protocol, widening the range of its applicability.

Topological phase transition of the generalized Su–Schrieffer–Heeger model based on a frequency-modulated circuit quantum electrodynamics lattice

We propose a scheme to investigate the topological phase transition in the generalized one-dimensional Su–Schrieffer–Heeger (SSH) model based on a circuit quantum electrodynamics (QED) lattice with frequency modulation. We find that, if we keep the resonant counter rotating wave terms to map the p-wave superconducting pairing terms in the topological superconductor by dint of frequency modulation, the circuit QED lattice can be equivalent to the SSH model with p-wave superconducting pairing terms. The numerical results show that the existence of the superconducting pairing terms cannot close the energy gap of the SSH model within the feasible range of parameters, which means that the superconducting pairing terms cannot induce the topological phase transition. To induce the topological phase transition, we add the next-nearest-neighboring (NNN) interaction into the circuit QED-based SSH model simultaneously. We find that, for a given superconducting pairing strength, the appropriate selection of the NNN interaction can induce closing of the energy gap. It indicates that a new topological phase transition between the topologically nontrivial SSH phase and the topologically trivial SSH phase occurs in the SSH model. Our scheme provides a means to explore the topological SSH phase transition based on a circuit QED lattice with frequency modulation.

Skyrmion Crystals and Phase Transitions in Magneto-Ferroelectric Superlattices: Dzyaloshinskii–Moriya Interaction in a Frustrated J1 − J2 Model

The formation of a skyrmion crystal and its phase transition are studied, taking into account the Dzyaloshinskii–Moriya (DM) interaction at the interface between a ferroelectric layer and a magnetic layer in a superlattice. Frustration is introduced in both magnetic and ferroelectric films. The films have a simple cubic lattice structure. The spins inside the magnetic layers are Heisenberg spins interacting with each other via nearest-neighbor (NN) exchange J m and next-nearest-neighbor (NNN) exchange J 2 m . The polarizations in the ferroelectric layers are assumed to be of Ising type with NN and NNN interactions J f and J 2 f . At the magnetoelectric interface, a DM interaction J m f between spins and polarizations is supposed. The spin configuration in the ground state is calculated by the steepest descent method. In an applied magnetic field H perpendicular to the layers, we show that the formation of skyrmions at the magnetoelectric interface is strongly enhanced by the frustration brought about by the NNN antiferromagnetic interactions J 2 m and J 2 f . Various physical quantities at finite temperatures are obtained by Monte Carlo simulations. We show the critical temperature, the order parameters of magnetic and ferroelectric layers as functions of the interface DM coupling, the applied magnetic field, and J 2 m and J 2 f . The phase transition to the disordered phase is studied in detail.

On the separation of time scales close to a glass transition: results from quench studies of the next-nearest-neighbour Ising model

Simulated quench studies of the next-nearest-neighbour (nnn) Ising model demonstrate the separation of time scales corresponding to the order parameter of the ground states and to the orientational order parameter as the value of the nnn interaction parameter approaches the critical value at which the glass transition occurs. Simply defined characteristic times, corresponding to both short-time processes (fast dynamics) and long-time processes (slow dynamics), are used to illustrate this separation and to elucidate the nature of the glass transition for this model. In particular, it is shown that the orientational order parameter remains nonzero at low temperature even at the critical value of the nnn interaction parameter (i.e., for K = Kc). Implications for the study of nonequilibrium effects in systems with striped ground states are discussed.

Hückel Molecular Orbital Quantities of {X,Y}-Cyclacene Graphs Under Next-Nearest-Neighbour Approximations in Analytical Forms

Abstract Hückel molecular orbital (HMO) quantities, viz., electron densities, charge densities, bond orders, free valences, total π-electron energies and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) or band gaps of {X,Y}-cyclacene graphs under next-nearest-neighbour (nnn) approximations are expressed in analytical forms within a certain range of nnn approximation parameter (m). The critical values of m for {X,Y}-cyclacenes with varying X (=C, N, B) and Y (=C, N, B) are calculated. For {X,X}-cyclacenes with a π-electron on each atom, all HMO quantities except total π-electron energies for a given value of m are found to be independent of X. The cyclic dimer (CD) is constructed in obtaining the eigenvalues corresponding to the singular points of the density of states (DOS) of such {X,Y}-cyclacene. Although the HOMO–LUMO gap of the CD differs from that of the cyclacene with a large number of repeating units (i.e. n ⟶ ∞) but becomes the same for m = 0. The analytical expressions can be used for facile computer programming in obtaining the HMO quantities. Such nnn interaction approximations actually release, to some extent, the strain that results in due to the geometrical structures of such cyclacenes, which is evident from the plots of strain energy per segment vs. contribution of such interactions on the total π-electron energy, where the slopes decrease with an increase in m. The vertical absorption energy difference for singlet-triplet states bears excellent linear correlation with the HOMO–LUMO gaps for a certain m value (m = 0.3) in the case of an even n, but for an odd n, such energy difference remains invariant.

The role of long relaxation times in a simple model with massless modes

The next-nearest-neighbour Ising model with competing nearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions, provides an example of a system in which massless modes destroy order at any finite temperature. This occurs only at a critical ratio, Kc, of the nnn and nn interactions. In this paper we investigate the role of long relaxation times in determining the behaviour of the system when the ratio of the nnn and nn interactions, K, is at and close to this critical ratio. Despite the absence of an order–disorder transition in systems with K = Kc, in Monte Carlo simulations reported here the temperature-dependent behaviour of the relaxation times indicates the existence of a glass transition with a glass transition temperature of Tg ≈ 0.26 in a model with nn interaction J = kB = 1.

Magnetization process and magnetocaloric effect in geometrically frustrated Ising antiferromagnet and spin ice models on a ‘Star of David’ nanocluster

Magnetic and magnetocaloric properties of geometrically frustrated antiferromagnetic Ising (IA) and ferromagnetic spin ice (SI) models on a nanocluster with a ‘Star of David’ topology, including next-nearest-neighbor (NNN) interactions, are studied by an exact enumeration. In an external field applied in characteristic directions of the respective models, depending on the NNN interaction sign and magnitude, the ground state magnetization of the IA model is found to display up to three intermediate plateaus at fractional values of the saturation magnetization, while the SI model shows only one zero-magnetization plateau and only for the antiferromagnetic NNN coupling. A giant magnetocaloric effect is revealed in the IA model with the NNN interaction either absent or equal to the nearest-neighbor coupling. The latter is characterized by abrupt isothermal entropy changes at low temperatures and infinitely fast adiabatic temperature variations for specific entropy values in the processes when the magnetic field either vanishes or tends to the critical values related to the magnetization jumps.

Effect of deposition rate and NNN interactions on adatoms mobility in epitaxial growth

This paper provides a detailed analysis of the surface diffusion problem during epitaxial step-flow growth using a simple theoretical model for the diffusion equation of adatoms concentration. Within this framework, an analytical expression for the adatom mobility as a function of the deposition rate and the Next-Nearest-Neighbor (NNN) interactions is derived and compared with the effective mobility computed from kinetic Monte Carlo (kMC) simulations. As far as the ‘small’ step velocity or relatively weak deposition rate commonly used for copper growth is concerned, an excellent quantitative agreement with the theoretical prediction is found. The effective adatoms mobility is shown to exhibit an exponential decrease with NNN interactions strength and increases in roughly linear behavior versus deposition rate F. The effective step stiffness and the adatoms mobility are also shown to be closely related to the concentration of kinks.

{X,Y}-Cyclacene Graphs with Next Nearest Neighbor Interactions

ABSTRACTEigensolutions of {X( = C,B,N),Y( = C,B,N)}-cyclacene graphs with next nearest neighbor (nnn) interactions have been obtained in analytical forms by adapting n-fold rotational symmetry followed by two-fold rotational symmetry (or a plane of symmetry). Expressions of eigensolution indicate the subspectral relationship among such cyclacenes with an even number of hexagonal rings e.g., eigenvalues of {X,Y}-di-cyclacene are found in the eigenspectra of all such even cyclacenes. Total π-electron energies and highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gaps are calculated using the analytical expressions obtained and are found to vary negligibly with the variation of nnn interactions in such cyclacenes. Total π-electron energy is found to increase due to increase in restriction intensity of nnn interactions, whereas the HOMO–LUMO gap of polyacenecs having the even number of hexagonal rings and with one electron at each site (atom) decreases with increase in the restriction intensity since such systems contain degenerate half-filled HOMO (bonding or nonbonding) that are much more vulnerable for perturbations imposed through nnn interactions.

Competing growth processes induced by next-nearest-neighbor interactions: Effects on meandering wavelength and stiffness

In this paper we explore the meandering instability of vicinal steps with a kinetic Monte Carlo simulations (kMC) model including the attractive next-nearest-neighbor (NNN) interactions. kMC simulations show that increase of the NNN interaction strength leads to considerable reduction of the meandering wavelength and to weaker dependence of the wavelength on the deposition rate F. The dependences of the meandering wavelength on the temperature and the deposition rate obtained with simulations are in good quantitative agreement with the experimental result on the meandering instability of Cu(0 2 24) [T. Maroutian et al., Phys. Rev. B 64, 165401 (2001)]. The effective step stiffness is found to depend not only on the strength of NNN interactions and the Ehrlich-Schwoebel barrier, but also on F. We argue that attractive NNN interactions intensify the incorporation of adatoms at step edges and enhance step roughening. Competition between NNN and nearest-neighbor interactions results in an alternative form of meandering instability which we call ``roughening-limited'' growth, rather than attachment-detachment-limited growth that governs the Bales-Zangwill instability. The computed effective wavelength and the effective stiffness behave as ${\ensuremath{\lambda}}_{\mathrm{eff}}\ensuremath{\sim}{F}^{\ensuremath{-}q}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\beta}}}_{\mathrm{eff}}\ensuremath{\sim}{F}^{\ensuremath{-}p}$, respectively, with $q\ensuremath{\approx}p/2$.

Scaling analysis of self-assembled structures and related morphological information in epitaxial growth

Using kinetic Monte-Carlo simulations, we have performed a qualitative and quantitative study of the homo-epitaxial growth for two materials Cu and Ag. Based on their dynamic scaling properties, a relationship between the resultant growth morphology and its computed scaling exponents is found to play a key role in the surface self-assembled at long time (hundreds of monolayer) and also at early time (sub-monolayer regime) of growth. Then, the effect of next-nearest-neighbor (NNN) interactions on the scaling exponents, as well as the surface morphology, is discussed. NNN interactions are found to affect the scaling exponents in the case of Cu rather than Ag. We also show that the higher the local roughness, the best 1-D nanostructures are obtained; which is confirmed by the measurement of filling rate of nanowires at step-edge on vicinal surfaces. Our results were compared to the available experimental and theoretical results and seem advantageous for a better understanding of the growth dynamics.

Collective transport of weakly interacting molecular motors with Langmuir kinetics

Filament-based intracellular transport involves the collective action of molecular motor proteins. Experimental evidences suggest that microtubule (MT) filament bound motor proteins such as kinesins weakly interact among themselves during transport and with the surrounding cellular environment. Motivated by these observations we study a driven lattice gas model for collective unidirectional transport of molecular motors on open filament. This model incorporates short-range next-nearest-neighbour (NNN) interactions between the motors and couples the transport process on filament with surrounding cellular environment through adsorption-desorption Langmuir kinetics (LK) of the motors. We analyse this model within the framework of a mean-field (MF) theory in the limit of weak interactions between the motors. We point to the mapping of this model with the non-conserved version of the Katz-Lebowitz-Spohn (KLS) model. The system exhibits rich phase behavior with a variety of inhomogeneous phases including localized shocks in the bulk of the filament. We obtain the steady-state density and current profiles, analyse their variation as a function of the strength of interaction and construct the non-equilibrium MF phase diagram. We compare these MF results with Monte Carlo simulations and find that the MF analysis shows reasonably good agreement with simulation results as long as the motors are weakly interacting. For sufficently strong NNN interaction between the motors, the mean-field results deviate significantly, and for very strong NNN interaction in the absence of LK, the current in the lattice is determined solely by the NNN interaction parameter and it becomes independent of entry and exit rates of motors at the filament boundaries.

Interaction-driven phases in a Dirac semimetal: exact diagonalization results

The interaction-driven phases in the Dirac semimetal (SM) of the π-flux model on the square lattice are studied with nearest-(NN), next-nearest-(NNN) and next-next-nearest-neighbor (NNNN) interactions using the exact diagonalization method. We find that the NN interaction drives a phase transition from the SM phase to a charge density wave insulator. In the presence of the NNN interaction, the system becomes an anisotropic SM for small interactions and an insulator with the stripe order for large ones. The NNNN interaction drives the Dirac SM to a dimmerized insulator. The interplay of the NNN and NNNN interactions is also studied. We find that the NNNN interaction firstly eliminates the effect of the NNN interaction and then develops its favorable order. In the calculations, the signature of the interaction-driven quantum anomalous Hall phase is not found.

Monte Carlo simulations of polymers with nearest- and next nearest-neighbor interactions on square and cubic lattices

We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases separated by continuous transition lines. Along these lines, we calculate the metric νt, crossover ϕt and entropic γt exponents, all of them in good agreement with the exact values of the Θ universality class. Therefore, the introduction of NNN interactions does not change the class of the ISAW model, which still exists even for repulsive forces. The growth parameters μt are shown to change monotonically with temperature along the Θ-lines. In the square lattice, the Θ-line has an almost linear behavior, which was not found in the cubic one. Although the region of repulsive NNN interactions, with attractive NN ones, leads to stiff polymers, no evidence of a transition to a crystalline phase was found.

Spin transport of the frustrated integer spin S antiferromagnetic Heisenberg chain

We study the effect of the nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions on spin transport in the quantum integer spin one-dimensional isotropic antiferromagnetic Heisenberg model. The Kubo formalism of the linear response theory is used to calculate the spin conductivity. We obtain the regular part of the spin conductivity, σreg(ω), as function of the frequency at T=0 and obtain a strong effect of the (nnn) interaction on magnon transport.

Asymmetrical Elementary Excitations Responsible for the Ferrimagnetism in an Antiferromagnetic Spin-1/2 Zigzag Ladder

The finite-temperature magnetic properties of an antiferromagnetic (AF) bond alternating S=1/2 zigzag spin chain with asymmetrical AF next-nearest-neighbor (NNN) exchange interactions in an external magnetic field are investigated by means of the many-body Greens function theory within random phase approximation. The results show that when the NNN exchange interactions are asymmetrical, the spin system exhibit a clear ferrimagnetic ordering at finite temperatures. It is shown that the ferrimagnetic behavior is attributed to asymmetrical elementary excitations, resulting from the competition between the spin frustrations and magnetic excitations reduced by the asymmetrical NNN interactions. The mechanism of this ferrimagnetism is much different from a common one which originates from mixed spins with different spin values through antiparallel spin alignments.

Temperature Dependence of Spin Excitations in the Frustrated Spin Chain System CuGeO3

We studied the temperature dependence of the spin excitation spectrum in the frustrated spin chain system CuGeO3 by a time-of-flight neutron scattering measurement. The intensity hump along the upper boundary (UB) of the continuum excitation, which is a robust feature for significant competition between next-nearest-neighbor (NNN) and nearest-neighbor (NN) exchange interactions, was shown to degrade upon warming. The hump disappears above ∼90 K, whereas the outline of the two-spinon continuum excitation remains even at 180 K. The decrease in intensity at the UB, the energy of which is >kBT (where kB and T are the Boltzmann constant and the temperature, respectively) for T<90 K, suggests that the contribution of NNN interaction to form the thermodynamic equilibrium state becomes negligible as a result of the thermal perturbation. The intensity of the lowest excited mode at the magnetic zone center weakens concomitantly with that at the UB. This intensity reduction, with remaining sizable energy-integrated ...