SOLITONS AND OTHER SOLUTIONS FOR THE (2+1)-DIMENSIONAL HEISENBERG FERROMAGNETIC SPIN CHAIN EQUATION USING IMPROVED MODIFIED EXTENDED TANH-FUNCTION METHOD

This paper studies $(2 + 1)$-dimensional Heisenberg ferromagnetic spin chain model by using improved modified extended tanh-function method. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic solutions, Weierstrass elliptic periodic type solutions and exponential function solutions. Moreover, some of the obtained solutions are represented graphically.

Thermal correlations and entropic uncertainty in a two-spin system under DM and KSEA interactions

In this paper, the thermal quantum correlations along with the thermal entropic uncertainty in a two neighboring XYZ Heisenberg spin-1/2 particles subjected to a transverse external magnetic field with the interplay of both antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony are investigated. The quantum consonance and uncertainty-induced quantum nonlocality as well as the entropic uncertainty with quantum memory for the considered system are specified and the thermal behaviors of them in terms of the system parameters are examined. The expected decrease of quantum correlations for higher absolute temperatures is confirmed while the inflation of the uncertainty is generated. Moreover, we show that the stronger spin-spin and spin-orbit exchange couplings can enhance the thermal quantum correlations and suppress the uncertainty. Accordingly, our remarks are expected to be beneficent in illustrating the dynamical quantum correlations and entropy-based uncertainty in a general Heisenberg spin-chain model and thus would be useful for practical quantum information processing.

The Yangian relations of Heisenberg spin chain model

In this paper, we investigate the Yangian relations of Heisenberg spin chain systems. Firstly, we consider the closed XXZ spin chain model, through the Heisenberg spin XXZ model, we found the Hamiltonians for one kind system of three adjacent partial particles interaction systems. The model’s constitution rules of energy levels and energy states which expand from the few-particle system to multi-particle system have good regularity. In this system, we found Yangian’s law and illustrate it through graphs. Secondly, we further consider the closed XXZ spin chain’s generalization of other three neighboring particles interaction systems from few-particle system to multi-particle system. Finally, we also discussed the laws of the three adjacent particles system of some models, they are the XXZ model with twist boundary condition, the open XXZ spin chain model and the XXZ model containing the next neighbor. In addition, not only XXZ model, XXX model, XY model and Ising model, but the relevant laws of spin-1 systems of these models were also discussed, they have similar rules to the XXZ model. Through calculation and research, the eigensystems of these models all have good Yangian and constitution laws.

Symmetry decomposition of relative entropies in conformal field theory

We consider the symmetry resolution of relative entropies in the 1+1 dimensional free massless compact boson conformal field theory (CFT) which presents an internal U(1) symmetry. We calculate various symmetry resolved Rényi relative entropies between one interval reduced density matrices of CFT primary states using the replica method. By taking the replica limit, the symmetry resolved relative entropy can be obtained. We also take the XX spin chain model as a concrete lattice realization of this CFT to perform numerical computation. The CFT predictions are tested against exact numerical calculations finding perfect agreement.

Measure of unevenness in human genomes, described as a self-affine phase transition in a 'spin-chain’ model

Background: Non-Gaussian distribution of polymorphic positions across a genome can substantially influence the results of any approach to molecular evolution based on a 'classical' probability model. The infinite dispersion of non-Gaussian perturbations is a challenge in an attempt to accept it in a probability-based model of evolution. Methods: Here a model is proposed where non-Gaussian distribution is introduced to an exact solution of the 'Ising model'; it describes a behavior of one-dimensional chain of spins in an approaching to a phase transition. The distribution of fragments which are identical between two genomes is similar to distribution of islands of spins with the same orientation, in the model where non-integer dimension is introduced. Results: Application of this model allows us to compare the relative contributions of non-Gaussian perturbations for pairs of human genomes from different ethnic groups. An evolution of the three human races in a most compact presentation is considered, rates of development on the separated stages of the evolution are assumed to be proportional to a value of relative unevenness between the appropriate groups of genomes. In the resolved model, the meaningful details of the separation between Asian and European races are clarified, in a period around ten thousand years ago; a particular viewpoint to the separation of the African race is also presented. Conclusion: The proposed approximation of non-Gaussian perturbations in human genomes allows to support the statements which are otherwise missed in the scientific investigations of the early history of modern humans.