Next-nearest Neighbor Interactions Research Articles

Universal behavior of the Shannon mutual information in nonintegrable self-dual quantum chains

An existing conjecture states that the Shannon mutual information contained in the ground state wavefunction of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the von Neumann entanglement entropy, depends on the value of the central charge of the underlying conformal field theory describing the physical properties. This conjecture applies whenever the ground state wavefunction is expressed in some special basis (conformal basis). Its formulation comes mainly from numerical evidences on exactly integrable quantum chains. In this paper the above conjecture was tested for several general non-integrable quantum chains. We introduce new families of self-dual $Z(Q)$ symmetric quantum chains ($Q=2,3,\ldots$). These quantum chains contain nearest neighbour as well next-nearest neighbour interactions (coupling constant $p$). In the cases $Q=2$ and $Q=3$ they are extensions of the standard quantum Ising and 3-state Potts chains, respectively. For $Q=4$ and $Q\geq 5$ they are extensions of the Ashkin-Teller and $Z(Q)$ parafermionic quantum chains. Our studies indicate that these models are interesting on their own. They are critical, conformally invariant, and share the same universality class in a continuous critical line. Moreover, our numerical analysis for $Q=2-8$ indicate that the Shannon mutual information exhibits the conjectured behaviour irrespective if the conformally invariant quantum chain is exactly integrable or not. For completeness we also calculated, for these new families of quantum chains, the two existing generalizations of the Shannon mutual information, which are based on the R\'enyi entropy and on the R\'enyi divergence.

Knots in finite memory walks

We investigate the occurrence and size of knots in a continuum polymer model with finite memory via Monte Carlo simulations. Excluded volume interactions are local and extend only to a fixed number of successive beads along the chain, ensuring that at short length scales the excluded volume effect dominates, while at longer length scales the polymer behaves like a random walk. As such, this model may be useful for understanding the behavior of polymers in a melt or semi-dilute solution, where exactly the same crossover is believed to occur. In particular, finite memory walks allow us to investigate the role of local interactions in the transition from highly knotted ideal polymers to almost unknotted self-avoiding polymers. Even though knotting decreases substantially when a few next-nearest neighbor interactions are considered, we find that the knotting probability of a polymer chain of modest length of 500 steps only decays slowly as a function of the range of the excluded volume interaction. In this context, we also find evidence that for length scales up to the interaction length the knotting behavior of the finite memory walk resembles that of a self-avoiding walk (effectively suppressing small knots), while for larger length scales it resembles that of a random walk.

Evolution of thermodynamic properties and inelastic neutron scattering intensities for spin-12antiferromagnetic quantum rings

This study examines the increasing complexity in the magnetic properties of small $n$ = 3, 4, 5, 6 spin-1/2 quantum rings. Using an exact diagonalization of the isotropic Heisenberg Hamiltonian with nearest and next-nearest neighbor interactions, the energy eigenstates, magnetic specific heat capacity, magnetic susceptibility, and inelastic neutron scattering structure factors are determined for variable next-nearest neighbor interactions. Here, it is shown that the presence of a complex spin-mixing, multiple ground states, and non-zero ground states greatly complicate the spin Hamiltonian. Overall, the energy eigenstates and structure factor intensities are presented in closed form, while the thermodynamic properties detail the effect of a crossing interaction in the rings. The goal of this work is to provide insight into the evolution of the magnetic properties and spin excitations within these systems.

Dimerization transitions in spin-1 chains

We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest neighbor (NNN) and 3-site interactions using extensive numerical simulations and a conformal field theory analysis. We show that the transition can be second order in the WZW SU(2)$_2$ or Ising universality class, or first-order. We argue that these features are generic because of a marginal operator in the WZW SU(2)$_2$ model, and because of two topologically distinct non-dimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.

Critical and compensation points of a mixed spin-2-spin-5/2 Ising ferrimagnetic system with crystal field and nearest and next-nearest neighbors interactions

We perform Monte Carlo simulations to analyze the magnetic properties of a mixed Ising model, where spins S that can take 5 values , 0,±1,±2, alternate on a square lattice with spins σ that can take 6 values, ±5/2,±3/2,±1/2. The Hamiltonian of the model includes an antiferromagnetic interaction between the S and σ spins, nearest-neighbors on the lattice, a ferromagnetic interaction between the S spins, next-nearest neighbors on the lattice, and a crystal field. We found that the system presents compensation temperatures in a wide range of the parameters. At the compensation temperature the total magnetization is zero but, contrary to what happens at the critical temperature, the system remains ordered. These temperatures have important technological applications, particularly in the field of thermo-magnetical recording. We calculate the finite-temperature phase diagram of the model. We found that the presence of the compensation temperature is strongly dependent on the next-nearest neighbor interaction term between the S spins, while its value can be calibrated by changing the crystal field.

Electric polarization observed in single crystals of multiferroicLu2MnCoO6

We report electric polarization and magnetization measurements in single crystals of double perovskite Lu2MnCoO6 using pulsed magnetic fields and optical second harmonic generation (SHG) in DC magnetic fields. we observe well-resolved magnetic field-induced changes in the electric polarization in single crystals and thereby resolve the question about whether multiferroic behavior is intrinsic to these materials or an extrinsic feature of polycrystals. We find electric polarization along the crystalline b-axis, that is suppressed by applying a magnetic fields along c-axis and advance a model for the origin of magnetoelectric coupling. We furthermore map the phase diagram using both capacitance and electric polarization to identify regions of ordering and regions of magnetoelectric hysteresis. This compound is a rare example of coupled hysteretic behavior in the magnetic and electric properties. The ferromagnetic-like magnetic hysteresis loop that couples to hysteretic polarization can be attributed not to ordinary ferromagnetic domains, but to the rich physics of magnetic frustration of Ising-like spins in the axial next-nearest neighbor interaction model.

Spatially frustrated S=1 Heisenberg antiferromagnet with single ion anisotropy

Using the SU(3) Schwinger boson formalism, I study the S=1 square lattice Heisenberg antiferromagnet, at zero temperature, with spatially anisotropic nearest-neighbor couplings frustrated by a next-nearest neighbor interaction and single ion anisotropy. The phase diagram at zero temperature is presented. My calculations show two magnetically ordered phases separated by a quantum-disordered region for all values of the anisotropy.

Repulsive Interactions Induced by Specific Adsorption: Anomalous Step Diffusivity and Inadequacy of Nearest-Neighbor Ising Model (Part II Theory)

This is Part II of two closely related papers, where we show that the strong repulsive interaction caused by specifically adsorbed anions leads to a failure of the nearest-neighbor Ising model to describe structures on electrode surfaces. In this part, an analytical form of the step diffusivity is derived in terms of nearest and next-nearest neighbor interactions for steps with a mean direction along 〈110〉 (the close-packed direction). With the help of a further analytical expression for the diffusivity of steps with 〈100〉 mean orientation a simple scheme is developed whereby the nearest and next-nearest interaction energies can be extracted from the experimental values for the diffusivity along the 〈110〉- and 〈100〉-directions. The method is applicable to repulsive and attractive next-nearest neighbor interactions, both for surfaces in vacuum and in contact with an electrolyte. An example is presented in Part I, where we apply our approach to Au(100) in Br--, Cl-- and SO42—containing electrolytes.

Repulsive interactions induced by specific adsorption: Anomalous step diffusivity and inadequacy of nearest-neighbor Ising model: (part I experimental)

This is Part I of two closely related papers, where we show that the specific adsorption of anions leads to a failure of the nearest-neighbor Ising model to describe island perimeter curvatures on Au(100) electrodes in dilute KBr, HCl and H2SO4 electrolytes and the therewith derived step diffusivity vs. step orientation. This result has major consequences for theoretical studies aiming at the understanding of growth, diffusion and degradation phenomena. Part I focuses on the experimental data.As shown theoretically in detail in Part II (doi:10.1016/j.susc.2016.03.022), a set of nearest-neighbor and next-nearest-neighbor interaction energies (ϵNN, ϵNNN) can uniquely be derived from the diffusivity of steps along 〈100〉 and 〈110〉. We find strong repulsive next-nearest neighbor (NNN) interaction in KBr and HCl, whereas NNN interaction is negligibly for H2SO4. The NNN repulsive interaction energy ϵNNN therefore correlates positively with the Gibbs adsorption energy of the anions. We find furthermore that ϵNNN increases with increasing Br− and Cl− coverage.The results for ϵNNand ϵNNN are quantitatively consistent with the coverage dependence of the step line tension. We thereby establish a sound experimental base for theoretical studies on the energetics of steps in the presence of specific adsorption.

Thermodynamic, critical properties and phase transitions of the Ising model on a square lattice with competing interactions

Abstract The thermodynamic and critical properties, and phase transitions of two-dimensional Ising model on a square lattice with competing interactions are investigated by the Monte Carlo method. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r = J 2 / J 1 in the value ranges of 0.1≤ r ≤1.0. The anomalies of thermodynamic observables are shown to be present in this model on the interval 0.45≤ r ≤0.5. The phase diagram for the dependence of the critical temperature on a value of next-nearest neighbor interaction is plotted. A phase transition for all values in the interval 0.45≤ r ≤0.5 is shown to be a second order. Our data show that the temperature of the heat capacity maximum at r =0.5 tends to a finite value. The static critical exponents of the heat capacity α , susceptibility γ , order parameter β , correlation length ν , and the Fisher exponent η are calculated by means of the finite-size scaling theory. It is found that the change in next-nearest neighbor interaction value in the range 0.7≤ r ≤1.0 leads to nonuniversal critical behavior.

Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J1 and J2, respectively. PTs in these models are analyzed for the ratio r = J2/J1 of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J1 0 and J2 < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.

Variational identification of a fractional Chern insulator in an extended Bose-Hubbard model

We study the extended Bose-Hubbard model on the square lattice at half filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a two-parameter family of wave-functions based on the parton construction which can describe both topological and broken symmetry phases on equal footing. In addition, our wave-functions resolve long standing issues with more conventional short-range Jastrow wave-functions. Using this variational ansatz, we show that a spontaneous time-reversal symmetry breaking fractional Chern insulator is energetically favored over a critical region between two superfluid phases. In verifying the properties of these parton wave-functions we exemplify a more robust way to identify topology through the Hall conductance.

Highly Anisotropic Magnon Dispersion in Ca_{2}RuO_{4}: Evidence for Strong Spin Orbit Coupling.

The magnon dispersion in Ca_{2}RuO_{4} has been determined by inelastic neutron scattering on single crytals containing 1% of Ti. The dispersion is well described by a conventional Heisenberg model suggesting a local moment model with nearest neighbor interaction of J=8 meV. Nearest and next-nearest neighbor interaction as well as interlayer coupling parameters are required to properly describe the entire dispersion. Spin-orbit coupling induces a very large anisotropy gap in the magnetic excitations in apparent contrast with a simple planar magnetic model. Orbital ordering breaking tetragonal symmetry, and strong spin-orbit coupling can thus be identified as important factors in this system.

Dynamical phases in a one-dimensional chain of heterospecies Rydberg atoms with next-nearest-neighbor interactions

We theoretically investigate the dynamical phase diagram of a one-dimensional chain of laser-excited two-species Rydberg atoms. The existence of a variety of unique dynamical phases in the experimentally-achievable parameter region is predicted under the mean-field approximation, and the change of those phases when the effect of the next-nearest neighbor interaction is included is further discussed. In particular we find the competition of the strong Rydberg-Rydberg interactions and the optical excitation imbalance can lead to the presence of complex multiple chaotic phases, which are highly sensitive to the initial Rydberg-state population and the strength of the next-nearest neighbor interactions.

Influence of next-nearest neighbor interaction on low temperature properties of the spin-1/2 one-dimensional ferromagnetic XY model

In this paper, we apply spin-wave theory to the one-dimensional spin-1/2 ferromagnetic XY model with the next-nearest neighbor interaction. The thermodynamic divergences which the conventional spin-wave theory encounters with, are solved by implementing Takahashi’s idea through introducing a Lagrange multiplier in the Hamiltonian to keep zero magnetization. It is shown that the next-nearest neighbor interaction has an influence on the ground-state and low temperature properties of the system. The exponential laws which are induced by the next-nearest neighbor interaction, are found for heights of maxima of the specific heat and its coefficient, as well as the maximum and minimum of the susceptibility coefficient. The maximum positions of the specific heat and its coefficient fit well to the linear and exponential laws under the next-nearest neighbor interaction, respectively.

Quantum signature of discrete breathers in a nonlinear Klein–Gordon lattice with nearest and next-nearest neighbor interactions

A theoretical work on quantum breathers in a nonlinear Klein–Gordon lattice model with nearest and next-nearest neighbor interactions is presented. The semiclassical and the full quantum cases are respectively considered. For the semiclassical case, we obtain the analytical solution of discrete breather, and find that the wave number corresponding to the appearance of discrete breather changes when the ratio of the next-nearest- to -nearest - neighbor harmonic force constants is greater than 1/4. For the full quantum case, by calculating the energy spectrum of the system containing two quanta, we prove numerically the existence of quantum breathers (two-quanta bound states) and find the shape of energy spectrum changes dramatically as the value of next -nearest neighbor harmonic force constant increasing.

Mixed-mode translaminar fracture of woven composites using a heterogeneous spring network

A statistical approach is taken to model the complex fracture process involved in the mode-I and mixed-mode translaminar growth of a macroscopic crack in a representative woven composite material. A two dimensional rectangular elastic spring network with nearest and next-nearest neighbour interactions was used to discretise a typical fracture specimen. An arrangement of rigid truss elements was introduced at the top and bottom edges of the network to model the displacement boundary conditions realistically. Heterogeneous properties of the woven composites were incorporated in the model by defining four types of regions composed of different combinations of hard and soft bonds. Among the model parameters, the ratio between the modulus of hard and soft bonds was found to have minimal effect on the fracture process as well as the macroscopic response. However, the ratio between the mean failure threshold strains is shown to be critical in simulating nucleation of damage at multiple sites around the initial crack plane resulting in large process zones and higher dissipation of energy during crack growth that is typical of composite materials as reported in existing literature.

Fidelity study of superconductivity in extended Hubbard models

The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground-state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest and next-nearest neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they are attractive or repulsive, seemingly due to competing charge fluctuations.

Phase Transitions in Frustrated Ising Antiferromagnet on a Body-Centered Cubic Lattice with Next-Nearest Neighbor Interactions

The phase transitions in antiferromagnetic Ising model are studied on a body-centered cubic lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transitions of second order. A static magnetic critical indices is calculated using the finite-dimensional scaling theory.

Thermalization away from integrability and the role of operator off-diagonal elements.

We investigate the rate of thermalization of local operators in the one-dimensional anisotropic antiferromagnetic Heisenberg model with next-nearest neighbor interactions that break integrability. This is done by calculating the scaling of the difference of the diagonal and canonical thermal ensemble values as a function of system size, and by directly calculating the time evolution of the expectation values of the operators with the Chebyshev polynomial expansion. Spatial and spin symmetry is exploited and the Hamiltonian is divided into subsectors according to their symmetry. The rate of thermalization depends on the proximity to the integrable limit. When integrability is weakly broken thermalization is slow, and becomes faster the stronger the next-nearest neighbor interaction is. Three different regimes for the rate of thermalization with respect to the strength of the integrability breaking parameter are identified. These are shown to be directly connected with the relative strength of the low and higher energy difference off-diagonal operator matrix elements in the symmetry eigenbasis of the Hamiltonian. Close to the integrable limit the off-diagonal matrix elements peak at higher energies and high-frequency fluctuations are important and slow down thermalization. Away from the integrable limit a strong low-energy peak gradually develops that takes over the higher frequency fluctuations and leads to quicker thermalization.