Exact eigenstates and magnetic response of spin-1 and spin-2 bose-einstein condensates

The exact eigenspectra and eigenstates of spin-1 and spin-2 Bose-Einstein condensates (BECs) are found, and their response to a weak magnetic field is studied and compared with their mean-field counterparts. Whereas mean-field theory predicts the vanishing population of the zero magnetic-quantum-number component of a spin-1 antiferromagnetic BEC, the component is found to become populated as the magnetic field decreases. The spin-2 BEC exhibits an even richer magnetic response due to quantum correlations among three bosons.     

Acoustic spin-1 Weyl semimetal

The study of topological semimetals hosting spin-1 Weyl points(WPs) beyond Dirac points and WPs has attracted a great deal of attention. However, a spin-1 Weyl semimetal that exclusively possesses spin-1 WPs in a clean frequency window without being shadowed by any other nodal points is yet to be discovered. This study reports a spin-1 Weyl semimetal in a phononic crystal. Its spin-1 WPs are touched by two linear dispersions and an additional flat band and carry monopole charges(-2,0,2) or(2,0,-2) for the three bands from the bottom to the top. They result in double Fermi arcs, which occur between the first and second bands, as well as between the second and third bands. Further robust propagation is observed against the multiple joints and topological negative refraction of the acoustic surface arc wave. The results of this study create the basis for the exploration of the unusual properties of spin-1 Weyl physics on a macroscopic scale.     

Exploring the entanglement of free spin-(1/2), spin-1 and spin-2 fields

In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.     

Thermodynamic properties of the mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies is solved exactly by means of a mapping to the spin-1/2 Ising chains with alternating transverse fields and the Jordan-Wigner transformation. Within this scheme, the thermodynamic quantities of this model are rigorously determined by a recursion formula derived for the partition function based on the reduced spin-1/2 transverse Ising model. The corresponding thermodynamic properties are calculated and discussed.     

Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.      

Green's function study of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system

The magnetic properties of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system on a square lattice are investigated by using the double-time temperature-dependent Green's function technique. In order to decouple the higher order Green's functions, Anderson and Callen's decoupling and random phase approximations have been used. The nearest- and next-nearest-neighbor interactions and the single-ion anisotropies are considered and their effects on compensation and critical temperature are studied.     

Effective-field and Monte Carlo studies of mixed spin-2 and spin-1/2 Ising diamond chain

The magnetic properties of a mixed spin-2 and spin-1/2 ferromagnetic diamond chain are studied by effective-field theory and Monte Carlo(MC) simulation based on the Ising model.The temperature dependences of magnetization,magnetic susceptibility,internal energy,and specific heat are studied,respectively.The exchange interaction dependences of magnetization and the critical temperature are calculated by MC simulation.The changes of magnetization depending on the field increasing and then the field decreasing under steady-static conditions are also given.     

Electric and magnetic polarizabilities of pointlike spin-1/2 particles

The electric and magnetic polarizabilities of pointlike spin-1/2 particles with an anomalous magnetic moment (AMM) are calculated by the transformation of an initial Hamiltonian into the Foldy-Wouthuysen (FW) representation. Corresponding results for spin-1/2 and spin-1 particles are compared.     

Cartan's contortion as a system of spin-2 and spin-0 fields

In several previous papers the author proposed to consider Cartan's contortion as a gauge field of Lorentz-group mediated by a massless spin-2 fields twin. In this article it is shown that these fields may be accompanied by a further pair of massive or massless spin-0 fields. Unfortunately, the study of the interaction of contortion with a Proca field shows that there is no reasonable macroscopic source generating the contortion. This defect is essential; the contortion mediated by standard fields can hardly exist in nature.     

Differential forms,spin-3/2 fields and Einstein's equations

The relationship between Einstein's vacuum field equations and classical spin-3/2 field equations is re-explored using two-component spinor valued differential forms. One-form and two-form expressions for spin-3/2 fields and their field equations are considered and a Lagrangian formulation is presented. Complex structures defined by spin-3/2 fields are considered.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments (MMs) in terms of Chiral Perturbation Theory (ChPT).In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ++ and Δ + are found to agree well with data within the experimental uncertainties.     

Minimal coupling in spin-2 field

It is shown that the spin-2 Lagrangian of Watanabe and Bhargava can be generalised by the introduction of a real parameter b associated with derivative ordering. After minimal coupling the spin-2 dynamical equations of Nath and Velo and Zwanziger can be derived as special cases. The constraint situation in these equations is then summarised and related to the first-order Lagrangian approach of Federbush, Chang, et al. Only one value of the parameter b gives a correct manifold of states after coupling. Finally it is shown that the auxiliary field approach to spin-2 proposed by Chang is dynamically inconsistent under minimal coupling.     

Using quaternions to design composite pulses for spin-1 NQR

The fictitious spin-1/2 operators are well known to describe the evolution of a pure nuclear quadrupole resonance (NQR) system; particularly, the application of a radio-frequency pulse at one of the NQR transition frequencies is equivalent to a three-dimensional rotation in a space defined by the corresponding fictitious spin-1/2 operators. We demonstrate, theoretically and experimentally, that consecutive noncommuting rotations applied at the same transition frequency are well described by a single rotation given by quaternion parameterization of the rotations in ficitious spin-1/2 operator space. This new route could greatly save computing time and efforts. We extend this approach to design composite pulses that compensate for the effects of the radio-frequency field inhomogeneity for a powder sample of spin-1 nuclei.     

Spin compensation temperatures in the mean-field approximation of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system

The magnetic behaviors of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system on a square lattice are studied with the mean-field approximation (MFA) based on the Bogoliubov inequality for the free energy. A Landau expansion of the free energy in the order parameter is also described in this work. In particular, we investigate the effect of a single-ion anisotropy on the compensation phenomenon.     

Automated computation of spin- and colour-correlatedBorn matrix elements

I report on an implementation of an algorithm for the automated numerical calculation of spin- and colour-correlated Born matrix elements in QCD. These spin- and colour-correlated matrix elements are needed for NLO calculations in combination with the subtraction method. Both massless and massive quarks are considered. There are no restrictions on the number of external particles. As a trivial sub-case, the algorithm also applies to Born matrix elements without any correlations. These are sufficient for leading order calculations.     

On properties of low-lying spin-1 hadron resonances

Properties of low-lying spin-1 hadron resonances are described in the review. It is shown how the Nambu–Jona-Lasinio model can be extended in the chiral invariant way by new tensor interactions. New mass formulas are obtained, which are not based on unitary symmetry groups but involve particles from different multiplets even with opposite parity. They all are in good agreement with experimental data. Dynamic properties of spin-1 mesons confirmed by the calculations performed using the QCD sum rule technique and the lattice calculations are understood and explained.     

Magnetic properties of a mixed spin-1/2 and spin-3/2 transverse Ising model

A theoretical study of a mixed spin-1/2 and spin-3/2 Ising system with independent transverse fields is presented using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the longitudinal and transverse components of the magnetization and its higher moments is also studied.     

Effective spin-2 quasi-particles at linear dispersive five-fold degenerate points with tunable topological Chern numbers

In this work, which is based on spin-2 vectors and traceless spin-2 tensors, an effective Hamiltonian is constructed with a linearly dispersive five-fold degenerate point with spin-2 vector-momentum couplings. For the model without spin-2 vector-tensor coupling, the topological Chern numbers of five bands are calculated as 4, 2, 0, ?2, ?4. After including spin-2 vector-tensor coupling, separate topological Chern numbers are obtained for different couplings. A cubic lattice of atoms with five internal states is designed to realize two five-fold degenerate points. The Chern numbers of the bands can be changed by tuning the coupling coefficient. In this work we propose a theoretical design to obtain spin-2 quasi-particles.     

Nonuniqueness of a massive spin-2 theory

The nonunique nature of massive spin-2 fields is explicitly shown in this paper through the construction of all possible field equations, using Dirac formalism for spin-1/2 fields. Out of these four possible theories, we point out two that do not show up scalar representations.     

Phase transitions and multicritical points in the mixed spin-3/2 and spin-2 Ising model with different single-ion anisotropies

The phase diagram of mixed spin-3/2 and spin-2 Ising ferromagnetic model with different single-ion anisotropies is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. Global phase diagrams are obtained in the temperature-anisotropy plane. In particular, by changing values of the single-ion anisotropies, several different types of phase diagrams of first-order transition between two ordered phases, are studied in detail. A variety of multicritical points such as tricritical points, isolated critical points, and triple points are obtained.