Spin Space Research Articles

Chiral Dirac Fermion in a Collinear Antiferromagnet

In a Dirac semimetal, the massless Dirac fermion has zero chirality, leading to surface states connected adiabatically to a topologically trivial surface state as well as vanishing anomalous Hall effect. Recently, it is predicted that in the nonrelativistic limit of certain collinear antiferromagnets, there exists a type of chiral “Dirac-like” fermion, whose dispersion manifests four-fold degenerate crossing points formed by spin-degenerate linear bands, with topologically protected Fermi arcs. Such an unconventional chiral fermion, protected by a hidden SU(2) symmetry in the hierarchy of an enhanced crystallographic group, namely spin space group, is not experimentally verified yet. Here, by angle-resolved photoemission spectroscopy measurements, we reveal the surface origin of the electron pocket at the Fermi surface in collinear antiferromagnet CoNb3S6. Combining with neutron diffraction and first-principles calculations, we suggest a multidomain collinear antiferromagnetic configuration, rendering the the existence of the Fermi-arc surface states induced by chiral Dirac-like fermions. Our work provides spectral evidence of the chiral Dirac-like fermion caused by particular spin symmetry in CoNb3S6, paving an avenue for exploring new emergent phenomena in antiferromagnets with unconventional quasiparticle excitations.

Rarita-Schwinger fields on nearly Kähler manifolds

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly Kähler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of Rarita-Schwinger fields coincides with the space of harmonic 3-forms. Applying the same technique to deformation theory, we also find that the space of infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of Killing spinors.

Zigzag materials: Selective interchain couplings control the coexistence of one-dimensional physics and deviations from it

The coexistence in the low-temperature spin-conducting phases of the zigzag materials BaCo2V2O8 and SrCo2V2O8 of one-dimensional (1D) physics with important deviations from it is not well understood. The studies of this paper account for an important selection rule that follows from interchain spin states being coupled more strongly within the spin dynamical structure factor of such zigzag materials whenever they are connected by a specific symmetry operation of the underlying lattice. In the case of excited states, this symmetry operation is only a symmetry in spin space if no electronic spin flip is performed within the generation of such states. The corresponding selective interchain couplings both protect the 1D physics and are behind important deviations from it concerning the enhancement of the spectral-weight intensity of Szz(k,ω). Strong evidence is provided that this justifies, beyond interchain mean-field theory and in contrast to 1D physics, the experimental low-energy dominance in both zigzag materials of the longitudinal nuclear magnetic resonance relaxation rate term 1/T1∥ for the whole magnetic field interval of the spin-conducting phases. To further understand the role of selective interchain couplings concerning their contradictory effects in protecting the 1D physics and controlling deviations from it, the physical-spins scattering processes behind the experimentally observed sharp peaks in the dynamic structure factor components are investigated. Indeed, the experimentally observed Bethe strings in S+−(k,ω) cannot be expressed in terms of configurations of usual spinons. We find that the line shape at and near the sharp peaks of the spin dynamic structure factor experimentally observed in BaCo2V2O8 and SrCo2V2O8 is fully controlled by unbound-unbound and unbound-bound scattering of singlet pairs of physical spins 1/2. Our results on both the role of selective interchain couplings in protecting the 1D physics and being behind deviations from it and on the dynamical properties being controlled by scattering of singlet pairs of physical spins 1/2 open the door to a key advance in the understanding of the physics of the spin chains in BaCo2V2O8 and SrCo2V2O8. Published by the American Physical Society 2023

Topological states protected by magnetic space groups and spin space groups

Topological states protected by magnetic space groups and spin space groups

Sea contribution to the charge radii and quadrupole moment of JP ½+, ³⁄₂+ baryons

Abstract An operator formalism is used on the wave function of baryons to compute their charge radii and quadrupole moments. The total anti-symmetric wave function in spin, color, and flavor space is framed for $J^P=\frac{1}{2}^+$ nucleons and $J^P=\frac{3}{2}^+$ hyperons. To understand the importance of the sea, a statistical model is used in conjugation with the detailed balance principle. Within the statistical approach, the importance of the sea with quarks and gluons are studied using the relevant probabilities that are associated with spin, flavor, and color space. The present work also focuses on individual contributions of valence and sea which contains terms of the scalar, vector, and tensor seas. The obtained results are in agreement with available theories and a few experimental outcomes. Our computed results may provide important information for upcoming experimental findings.

Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface

Abstract Inspired by the turf–ball interaction in golf, this paper seeks to understand the bounce of a ball that can be modelled as a rigid sphere and the surface as supplying a viscoelastic contact force in addition to Coulomb friction. A general formulation is proposed that models the finite time interval of bounce from touch-down to lift-off. Key to the analysis is understanding transitions between slip and roll during the bounce. Starting from the rigid-body limit with an energetic or Poisson coefficient of restitution, it is shown that slip reversal during the contact phase cannot be captured in this case, which generalizes to the case of pure normal compliance. Yet, the introduction of linear tangential stiffness and damping does enable slip reversal. This result is extended to general weakly nonlinear normal and tangential compliance. An analysis using the Filippov theory of piecewise-smooth systems leads to an argument in a natural limit that lift-off while rolling is non-generic and that almost all trajectories that lift off do so under slip conditions. Moreover, there is a codimension-one surface in the space of incoming velocity and spin which divides balls that lift off with backspin from those that lift off with topspin. The results are compared with recent experimental measurements on golf ball bounce and the theory is shown to capture the main features of the data.

Trajectorial Dissipation of {Phi }-Entropies for Interacting Particle Systems

A classical approach for the analysis of the long-time behaviour of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally Phi -entropies. Via purely analytic arguments it can be shown that these functionals are indeed non-increasing in time under quite general assumptions on the process. We refine these classical results via a more probabilistic approach and show that dissipation is already present on the level of individual trajectories for spatially extended systems of infinitely many interacting particles with arbitrary underlying geometry and compact local spin spaces. This extends previous results from the setting of finite-state Markov chains or diffusions in mathbb {R}^n to an infinite-dimensional setting with weak assumptions on the dynamics.

Invariant spinors on homogeneous spheres

Using the characterization of the spin representation in terms of exterior forms, we give a complete classification of invariant spinors on the nine homogeneous realizations of the sphere Sn. In each of the cases we determine the dimension of the space of such spinors, give their explicit description, and study the underlying related geometric structures depending on the metric. We recover some known results in the Sasaki and 3-Sasaki cases and find several new examples: in particular we give the first known examples of generalized Killing spinors with four distinct eigenvalues.

(Non-)unitarity of strictly and partially massless fermions on de Sitter space

We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin s = 3/2, 5/2 with any mass parameter on D-dimensional (D ≥ 3) de Sitter space (dSD) and Unitary Irreducible Representations (UIR’s) of the de Sitter algebra spin(D, 1). Our approach is based on expressing the eigenmodes on global dSD in terms of eigenmodes of the Dirac operator on the (D − 1)-sphere, which provides a natural way to identify the corresponding representations with known UIR’s under the decomposition spin(D, 1) ⊃ spin(D). Remarkably, we find that four- dimensional de Sitter space plays a distinguished role in the case of the gauge-invariant theories. In particular, the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields on dSD, are not unitary unless D = 4.

The Dirac equation on metrics of Eguchi–Hanson type

We investigate parallel spinors on the Eguchi–Hanson metrics and find the space of complex parallel spinors is complex two-dimensional. For the metrics of Eguchi–Hanson type with the zero scalar curvature, we separate variables for the harmonic spinors and obtain the solutions explicitly.

Interaction between spin and Abrikosov vortices in doped topological insulators

In the topological superconductor with the nematic superconductivity in $E_u$ representation, it is possible to have different types of vortices. One is associated with the vorticity in the particle-hole space and corresponds to the Abrikosov vortex. Another type corresponds to the vorticity in the spin space and is called spin vortex. We study the interaction of the Abrikosov vortex with the spin vortices. We derive the free energy of the sample with the Abrikosov and the strain-induced spin vortices using the Ginzburg-Landau approach for the two-component superconducting order parameter. We calculate the critical strain at which the spin vortex is formed. We show that the spin vortex and the Abrikosov vortex attract to each other and, as a result, they have a common core. We show that there are no zero-energy states (Majorana fermions) localized near the common vortex core of the Abrikosov vortex and the spin vortex of any type. Possible experimental realization is discussed.

Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transition and the second-order phase transition in XXZ models

We propose two machine-learning methods based on neural networks, which we respectively call the phase-classification method and the temperature-identification method, for detecting different types of phase transitions in the XXZ models without prior knowledge of their critical temperatures. The XXZ models have exchange couplings which are anisotropic in the spin space where the strength is represented by a parameter $\Delta(>0)$. The models exhibit the second-order phase transition when $\Delta>1$, whereas the Berezinskii-Kosterlitz-Thouless (BKT) phase transition when $\Delta<1$. In the phase-classification method, the neural network is trained using spin or vortex configurations of well-known classical spin models other than the XXZ models, e.g., the Ising models and the XY models, to classify those of the XXZ models to corresponding phases. We demonstrate that the trained neural network successfully detects the phase transitions for both $\Delta>1$ and $\Delta<1$, and the evaluated critical temperatures coincide well with those evaluated by conventional numerical calculations. In the temperature-identification method, on the other hand, the neural network is trained so as to identify temperatures at which the input spin or vortex configurations are generated by the Monte Carlo thermalization. The critical temperatures are evaluated by analyzing the optimized weight matrix, which coincide with the result of numerical calculation for the second-order phase transition in the Ising-like XXZ model with $\Delta=1.05$ but cannot be determined uniquely for the BKT transition in the XY-like XXZ model with $\Delta=0.95$.

Magnetic excitations in the helical Rashba superconductor

We investigate the magnetic excitation spectrum in the helical state of a noncentrosymmetric superconductor with inversion symmetry breaking and strong Rashba spin–orbit coupling. For this purpose we derive the general expressions of the dynamical spin response functions under the presence of strong Rashba splitting of conduction bands, superconducting gap and external field which lead to stabilization of Cooper pairs with finite overall momentum in a helical state. The latter is characterized by momentum space regions of paired and unpaired states with different quasiparticle dispersions. The magnetic response is determined by i) excitations within and between both paired and unpaired regions ii) anomalous coherence factors and iii) additional spin matrix elements due to helical Rashba spin texture of bands. We show that as a consequence typical correlated real space and spin space anisotropies appear in the dynamical susceptibility which would be observable as a characteristic fingerprint for a helical superconducting state in inelastic neutron scattering investigations.

Second release of the CoRe database of binary neutron star merger waveforms

We present the second data release of gravitational waveforms from binary neutron star (BNS) merger simulations performed by the Computational Relativity (CoRe) collaboration. The current database consists of 254 different BNS configurations and a total of 590 individual numerical-relativity simulations using various grid resolutions. The released waveform data contain the strain and the Weyl curvature multipoles up to . They span a significant portion of the mass, mass-ratio, spin and eccentricity parameter space and include targeted configurations to the events GW170817 and GW190425. CoRe simulations are performed with 18 different equations of state, seven of which are finite temperature models, and three of which account for non-hadronic degrees of freedom. About half of the released data are computed with high-order hydrodynamics schemes for tens of orbits to merger; the other half is computed with advanced microphysics. We showcase a standard waveform error analysis and discuss the accuracy of the database in terms of faithfulness. We present ready-to-use fitting formulas for equation of state-insensitive relations at merger (e.g. merger frequency), luminosity peak, and post-merger spectrum.

Vortex-bound solitons in topological superfluid 3He

The different superfluid phases of 3He are described by p-wave order parameters that include anisotropy axes both in the orbital and spin spaces. The anisotropy axes characterize the broken symmetries in these macroscopically coherent quantum many-body systems. The systems’ free energy has several degenerate minima for certain orientations of the anisotropy axes. As a result, spatial variation of the order parameter between two such regions, settled in different energy minima, forms a topological soliton. Such solitons can terminate in the bulk liquid, where the termination line forms a vortex with trapped circulation of mass and spin superfluid currents. Here we discuss possible soliton-vortex structures based on the symmetry and topology arguments and focus on the three structures observed in experiments: solitons bounded by spin-mass vortices in the B phase, solitons bounded by half-quantum vortices (HQVs) in the polar and polar-distorted A phases, and the composite defect formed by a half-quantum vortex, soliton and the Kibble-Lazarides-Shafi wall in the polar-distorted B phase. The observations are based on nuclear magnetic resonance (NMR) techniques and are of three types: first, solitons can form a potential well for trapped spin waves, observed as an extra peak in the NMR spectrum at shifted frequency; second, they can increase the relaxation rate of the NMR spin precession; lastly, the soliton can present the boundary conditions for the anisotropy axes in bulk, modifying the bulk NMR signal. Owing to solitons’ prominent NMR signatures and the ability to manipulate their structure with external magnetic field, solitons have become an important tool for probing and controlling the structure and dynamics of superfluid 3He, in particular HQVs with core-bound Majorana modes.

Algebra of the spinor invariants and the relativistic hydrogen atom

It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac Hamiltonian is invariant with respect to the rotation transformation, which indicates the dynamical (hidden) symmetry SU(2) of the Dirac equation. The total symmetry of the Dirac equation is the symmetry SO(3)⊗SU(2). The generator of the SO(3) symmetry group is given by the total momentum operator, and the generator of SU(2) group is given by the rotation of the vector-states in the spinor space, determined by the Dirac, Johnson–Lippmann, and the new spinor invariants. It is shown that using algebraic approach to the Dirac problem allows one to calculate the eigenstates and eigenenergies of the relativistic hydrogen atom and reveals the fundamental role of the principal quantum number as an independent number, even though it is represented as the combination of other quantum numbers.

Scrambling and entangling spinning particles

In this paper we revisit the gravitational eikonal amplitudes of two scattering spinning particles and inspect their scrambling power in the spin spaces that is quantified through the tripartite information. We found that in the non-relativistic limit and a special high-energy limit the leading contribution is a quantity that is universal and theory independent. The minimal coupling is singled out with minimal scrambling in a different high momenta limit. We also inspected the initial state dependence of entanglement generation and found that the spin coherent state with vanishing spin may not necessarily be the hardest to entangle. Interestingly, among a family of mixed states, the only P-rep state there known to be the best approximation of classical mixed states was singled out as one with minimal entanglement generated.

Algebraic geometry and p-adic numbers for scattering amplitude ansätze

Scattering amplitudes in perturbative quantum field theory exhibit a rich structure of zeros, poles and branch cuts which are best understood in complexified momentum space. It has been recently shown that by leveraging this information one can significantly simplify both analytical reconstruction and final expressions for the rational coefficients of transcendental functions appearing in phenomenologically-relevant scattering amplitudes. Inspired by these observations, we present a new algorithmic approach to the reconstruction problem based on p-adic numbers and computational algebraic geometry. For the first time, we systematically identify and classify the relevant irreducible surfaces in spinor space with five-point kinematics, and thanks to p-adic numbers – analogous to finite fields, but with a richer structure to their absolute value – we stably perform numerical evaluations close to these singular surfaces, thus completely avoiding the use of floating-point numbers. Then, we use the data thus acquired to build ansätze which respect the vanishing behavior of the numerator polynomials on the irreducible surfaces. These ansätze have fewer free parameters, and therefore reduced numerical sampling requirements. We envisage future applications to novel two-loop amplitudes.

Driven one-dimensional noisy Kitaev chain

We study a one-dimensional Kitaev chain driven by the anisotropy parameter ${J}_{\ensuremath{-}}=t/{\ensuremath{\tau}}_{Q}$, in the presence of weak Gaussian noise in the parameter ${J}_{+}$. The system is prepared in the ground state of the Hamiltonian at the initial time $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. The defect density and the residual energy at the end of the drive protocol reveals anti-Kibble Zurek (AKZ) behavior which deviates from the earlier reported linear in quench time dependence for the defect density. The entropy density at the end of the protocol is found to exhibit the signature of the AKZ behavior. In the context of the Kitaev chain, the two-point spin correlators are short ranged. The hidden topological order across the quantum phase transition point is probed via the nonlocal string order parameters. The two-point Majorana correlator and the hidden string correlator calculated in the final decohered state at the end of the noisy drive protocol is consistent with the AKZ picture. We have analyzed the kink statistics in the dual spin space, the first three cumulants at the end of the noisy drive also exhibit the AKZ scaling behavior for slower sweeps similar to the defect density. The kink distribution function is well approximated with the normal distribution with nonuniversal noise dependent mean and variance.

Spin 1/2 one‐ and two‐particle systems in physical space without eigen‐algebra or tensor product

Under the spin–position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra substitutes the vector–matrix spin model built on the Pauli spin operator. The standard quantum operator‐state spin formalism is replaced with vectors transforming by proper and improper rotations in the same 3D space—isomorphic to the space of Pauli matrices. In the single‐spin case, the novel spin 1/2 representation (1) is Hermitian, (2) shows handedness, (3) yields all the standard results and its modulus equals the total spin angular momentum , (4) formalizes irreversibility in measurement, and (5) permits adaptive imbedding of the 2D spin space in 3D. Maximally entangled spin pairs (1) are in phase and have opposite handedness, (2) relate by one of the four basic improper rotations in 3D: plane reflections (triplets) and inversion (singlet), (3) yield the standard total angular momentum, and (4) all standard expectation values for bipartite and partial observations follow. Depending on whether proper and improper rotors act one—or two—sided, the formalism appears in two complementary forms, the “spinor” or the “vector” form, respectively. The proposed scheme provides a clear geometric picture of spin correlations and transformations entirely in the 3D physical orientation space.