The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.     

Staggered anisotropy parameter modification of the anisotropic t–J model

The anisotropic t–J model (U_q(gl(2|1)) Perk–Schultz model) with staggered disposition of the anisotropy parameter along a chain is considered and the corresponding ladder type integrable model is constructed. This is a generalisation to spin-1 case of the staggered XXZ spin-1/2 model considered earlier. The corresponding Hamiltonian is calculated and, since it contains next to nearest neighbour interaction terms, can be written in a zig-zag form. The algebraic Bethe ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found.     

Slater determinant and exact eigenstates of the two-dimensional Fermi–Hubbard model

We consider the construction of exact eigenstates of the two-dimensional Fermi–Hubbard model defined on an L × L lattice with a periodic condition. Based on the characteristics of Slater determinants, several methods are introduced to construct exact eigenstates of the model. The eigenstates constructed are independent of the on-site electron interaction and some of them can also represent exact eigenstates of the two-dimensional Bose–Hubbard model.     

Study of supersolidity in the two-dimensional Hubbard–Holstein model

We derive an effective Hamiltonian for the two-dimensional Hubbard–Holstein model in the regimes of strong electron–electron and strong electron–phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a t₁ ? V ₁ ? V ₂ ? V ₃ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling 1∕8, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector \(\vec{Q}\) = (π∕4, 3π∕4) or (π∕4, 5π∕4). Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling 1∕8 and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.     

The Weiss model and the Landau–Khalatnikov model for the switching of ferroelectrics

It is shown that the molecular field theory by P. Weiss formally leads to the switching kinetics of ferroelectrics, which is described by the well-known Landau–Khalatnikov equation. The switching has a critical character, taking place only at E_a>E_c (E_a: external field, E_c: coercive field). The results are checked by computer simulations.     

Pseudo-ε-expansion and the two-dimensional Ising model

The pseudo-ε-expansions for the coordinate of the fixed point g^*, the critical exponents, and the sextic effective coupling constant g₆ are determined for the two-dimensional Ising model on the basis of the five-loop renormalization group series. It is found that the pseudoe-expansions for the coordinate of the fixed point g^*, the inverse exponent γ^?1, and the constant g₆ possess a remarkable property, namely, the higher terms of these series are so small that reliable numerical results can be obtained without invoking Borel summation.     

Construction of the two-dimensional sine-Gordon model for β<8π

We present a rigorous renormalization group construction of the two-dimensional massless and massive quantum sine-Gordon models in finite volume for the range 0<<8. We prove analyticity in the coupling constant , which implies the convergence of perturbation theory. The field correlation functions and their generating functional are analyzed and shown to have the short distance asymptotics of the free field theory. In the massive case the bounds are uniform in volume and we also obtain uniform estimates on the long distance decay of correlations.Research supported by NSF Grant PHY-9001178Research supported by the Natural Sciences and Engineering Research Council of Canada     

Universal probes of two-dimensional topological insulators: dislocation and π flux

We show that the π flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that π flux hosts a Kramers pair of zero modes in the topological Γ (Berry phase Skyrmion at the zero momentum) and M (Berry phase Skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a π flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.     

Simulation model of speed–density characteristics for mixed bicycle flow—Comparison between cellular automata model and gas dynamics model

The mixed bicycle flow refers to the bicycle flow containing electric bicycles. The traffic characteristics data of the mixed bicycle flow was collected by the virtual coil method in Nanjing and Ningbo, China. And the speed–density characteristics of the mixed bicycle flow with different proportions of electric bicycles were obtained. The results show that the overall speed of the mixed bicycle flow containing electric bicycles is higher than that of pure bicycle flow when the density is relatively low. The speed decreases when the density is higher than 0.08 bic/m²; the speed–density characteristics of the bicycles and the electric bicycles tend to be the same when the density is higher than 0.25 bic/m². And when the density reaches 0.58 bic/m², the mixed bicycle flow becomes blocked and the speed is zero. The cellular automata model and gas dynamics model were also adopted to simulate the speed–density characteristics of the mixed bicycle flow. The simulation results of the cellular automata model are effectively consistent with the actual survey data when the density is lower than 0.225 bic/m²; the simulation results of the gas dynamics model are effectively consistent with the actual survey data when the density is higher than 0.300 bic/m²; but both of the two types of simulation models are inapplicable when the density is between 0.225 and 0.300 bic/m². These results will be used in the management of mixed bicycles and the research of vehicle–bicycle conflict and so on.     

Zero- and low-temperature behavior of the two-dimensional ±J Ising spin glass

Scaling arguments and precise simulations are used to study the square lattice ±J Ising spin glass, a prototypical model for glassy systems. Droplet theory explains, and our numerical results show, entropically stabilized long-range spin-glass order at zero temperature, which resembles the energetic stabilization of long-range order in higher-dimensional models at finite temperature. At low temperature, a temperature-dependent crossover length scale is used to predict the power-law dependence on temperature of the heat capacity and clarify the importance of disorder distributions.     

Computer simulation study of the two-dimensional nematic lattice model based on the modified Gruhn–Hess pair potential model

A modified Gruhn–Hess pair potential model, where the potential parameters related to the elastic constants are different from the original model, was investigated with the aid of Monte Carlo (MC) simulation and Mean Field (MF) theory based upon a two-dimensional nematic lattice model. The model produces a ground state in perfect nematic order, where particles are aligned in the lattice plane. Both the MF predictions and the simulation results for the second-rank ordering tensor show that the system is biaxial in the low-temperature region, with a positive primary order parameter and the main director aligned along the lattice axis. A transition to uniaxial order takes place at higher temperatures with a negative primary order parameter and the director is orthogonal to the lattice plane. This orientational order survives up to temperatures higher than the transition temperature of the three-dimensional lattice model, possibly at all finite temperatures. MF predictions agree qualitatively with simulation but, in quantitative terms, the transition temperature is overestimated by 52%.     

A critical analysis and a recent improvement of the two-dimensional model for solution–precipitation creep: application to silicon nitride ceramics

The step model is one of the most widely used models of solution–precipitation creep in polycrystalline ceramics with secondary glassy phases. However, it leads to unrealistic stress exponent values when two-dimensional step nucleation takes place at the grain boundaries. We present a modification of the original model of step nucleation that avoids such unreasonable values by considering in detail the precipitation (or solution) process. The modified model agrees with reported experimental results for ceramic systems in which it has been accepted that high-temperature plasticity occurs by solution–precipitation.     

Modification of the Peierls–Nabarro model for misfit dislocation

For a misfit dislocation, the balance equations satisfied by the displacement fields are modified, and an extra term proportional to the second-order derivative appears in the resulting misfit equation compared with the equation derived by Yao et al. This second-order derivative describes the lattice discreteness effect that arises from the surface effect. The core structure of a misfit dislocation and the change in interfacial spacing that it induces are investigated theoretically in the framework of an improved Peierls–Nabarro equation in which the effect of discreteness is fully taken into account. As an application, the structure of the misfit dislocation for a honeycomb structure in a two-dimensional heterostructure is presented.     

Investigations of information quantifiers for the Tavis–Cummings model

In this article, a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via a multi-photon transition is considered. The quantum Fisher information, negativity, classical Fisher information, and reduced von Neumann entropy for the two atoms are investigated. We found that the number of photon transitions plays an important role in the dynamics of different information quantifiers in the cases of two symmetric and two asymmetric atoms. Our results show that there is a close relationship between the different quantifiers. Also, the quantum and classical Fisher information can be useful for studying the properties of quantum states which are important in quantum optics and information.