Arbitrary Spin Research Articles

Superfield approach to interacting N = 2 massive and massless supermultiplets in 3d flat space

Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N = 2 Poincaré superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generators of the N = 2 Poincaré superalgebra is also found.

Controllable spin current in van der Waals ferromagnet Fe3GeTe2

The control of spin current is pivotal for spintronic applications, especially for spin-orbit torque devices. Spin Hall effect (SHE) is a prevalent method to generate spin current. However, it is difficult to manipulate its spin polarization in nonmagnet. Recently, the discovery of spin current in ferromagnet offers opportunity to realize the manipulation. In the present work, the spin current in van der Waals ferromagnet Fe3GeTe2 (FGT) with varying magnetization is theoretically investigated. It has been observed that the spin current in FGT presents the nonlinear behavior with respect to magnetization. The in-plane and out-of-plane spin polarization emerges simultaneously, and the bilayer FGT can even exhibit arbitrary spin polarization thanks to the reduced symmetry. More intriguingly, the correlation between anomalous Hall effect (AHE) and spin anomalous Hall effect (SAHE) has been interpreted from the aspect of Berry curvature. This work illustrates that the interplay of symmetry and magnetism can effectively control the magnitude and spin polarization of the spin current, providing a practical method to realize exotic spin-orbit torques.

Dynamics of Colombo’s top: tidal dissipation and resonance capture, with applications to oblique super-Earths, ultra-short-period planets and inspiraling hot Jupiters

ABSTRACT We present a comprehensive theoretical study on the spin evolution of a planet under the combined effects of tidal dissipation and gravitational perturbation from an external companion. Such a ‘spin + companion’ system (called Colombo’s top) appears in many [exo]planetary contexts. The competition between the tidal torque (which drives spin-orbit alignment and synchronization) and the gravitational torque from the companion (which drives orbital precession of the planet) gives rise to two possible spin equilibria (‘tidal Cassini Equilibria’, tCE) that are stable and attracting: the ‘simple’ tCE1, which typically has a low spin obliquity, and the ‘resonant’ tCE2, which can have a significant obliquity. The latter arises from a spin-orbit resonance and can be broken when the tidal alignment torque is stronger than the precessional torque from the companion. We characterize the long-term evolution of the planetary spin (both magnitude and obliquity) for an arbitrary initial spin orientation, and develop a new theoretical method to analytically obtain the probability of resonance capture driven by tidal dissipation. Applying our general theoretical results to exoplanetary systems, we find that a super-Earth (SE) with an exterior companion can have a substantial probability of being trapped in the high-obliquity tCE2, assuming that SEs have a wide range of primordial obliquities. We also evaluate the recently proposed ‘obliquity tide’ scenarios for the formation of ultra-short-period Earth-mass planets and for the orbital decay of hot Jupiter WASP-12b. We find in both cases that the probability of resonant capture into tCE2 is generally low and that such a high-obliquity state can be easily broken by the required orbital decay.

On the group-theoretical approach to relativistic wave equations for arbitrary spin

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for arbitrary-spin particles are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the anti-de Sitter group leads to inconsistent results, mainly as a consequence of the violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

On the group-theoretical approach to relativistic wave equations for arbitrary spin

Формулировка релятивистского уравнения в случае частиц с произвольным спином остается открытой задачей в теоретической физике. Исследованы основные алгебраические подходы, позволяющие обобщить уравнения Дирака и Кеммера-Дэффина для произвольного спина частиц. Доказано, что неприводимое релятивистское уравнение, сформулированное с использованием матриц спина, удовлетворяющих коммутационным соотношениям группы анти-де Ситтера, приводит к противоречивым результатам, главным образом вследствие нарушения унитарности и появления спектра масс, который не отражает физическую природу элементарных частиц. Однако введение дополнительных условий решает проблему унитарности и восстанавливает физический смысл спектра масс. Найдены решения уравнений, полученных с помощью этих подходов, и обсуждается физическая природа решений.

Higher spin analogs of linearized topologically massive gravity and linearized new massive gravity

We suggest a new spin-4 self-dual model (parity singlet) and a new spin-4 parity doublet in $D=2+1$. They are of higher order in derivatives and are described by a totally symmetric rank-4 tensor without extra auxiliary fields. Despite the higher derivatives they are ghost free. We find gauge invariant field combinations which allow us to show that the canonical structure of the spin-4 (spin-3) models follows the same pattern of its spin-2 (spin-1) counterpart after field redefinitions. For $s=1$, 2, 3, 4, the spin-$s$ self-dual models of order $2s\ensuremath{-}1$ and the doublet models of order $2s$ can be written in terms of three gauge invariants. The cases $s=3$ and $s=4$ suggest a restricted conformal higher spin symmetry as a principle for defining linearized topologically massive gravity and linearized ``new massive gravity'' for arbitrary integer spins. A key role in our approach is played by the fact that the Cotton tensor in $D=2+1$ has only two independent components for any integer spin.

Self-dual models in [formula omitted] from dimensional reduction

Here we perform a Kaluza–Klein dimensional reduction of Vasiliev’s first-order description of massless spin-s particles from D=3+1 to D=2+1 and derive first-order self-dual models describing particles with helicities ±s for the cases s=1,2,3. In the first two cases we recover known (parity singlets) self-dual models. In the spin-3 case we derive a new first order self-dual model with a local Weyl symmetry which lifts the traceless restriction on the rank-3 tensor. A gauge fixed version of this model corresponds to a known spin-3 self-dual model. We conjecture that our procedure can be generalized to arbitrary integer spins.

Decoherence and objectivity in higher spin environments

We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of post-interaction environment states. This allows to analyze the objectivization process of the state of the central spin during the interaction. We do so using, so called, Spectrum Broadcast Structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-$1/2$ systems only, and we hope will be useful in future objectivity experiments.

Pseudospin symmetric solutions of the Dirac equation with the modified Rosen–Morse potential using Nikiforov–Uvarov method and supersymmetric quantum mechanics approach

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term, we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen–Morse potential including the spin–orbit coupling term by using the Nikiforov–Uvarov method and supersymmetric quantum mechanics approach. The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin–orbit coupling quantum number k are presented under the condition of pseudospin symmetry. The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations. The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.

AdS (super)projectors in three dimensions and partial masslessness

We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS3. The projectors are constructed in terms of the quadratic Casimir operators of the isometry group SO(2, 2) of AdS3. Their poles are demonstrated to correspond to (partially) massless fields. As an application, we make use of the projectors to recast the conformal and topologically massive higher-spin actions in AdS3 into a manifestly gauge-invariant and factorised form. We also propose operators which isolate the component of a field that is transverse and carries a definite helicity. Such fields correspond to irreducible representations of SO(2, 2). Our results are then extended to the case of mathcal{N} = 1 AdS3 supersymmetry.

Spinning black hole binary dynamics, scattering amplitudes, and effective field theory

We describe a systematic framework for finding the conservative potential of compact binary systems with spin based on scattering amplitudes of particles of arbitrary spin and effective field theory. An arbitrary-spin formalism is generally required in the classical limit. By matching the tree and one-loop amplitudes of four spinning particles with those of a suitably chosen effective field theory, we obtain the ${\mathrm{spin}}_{1}\text{\ensuremath{-}}{\mathrm{spin}}_{2}$ terms of a two-body effective Hamiltonian through $\mathcal{O}({G}^{2})$ and valid to all orders in velocity. Solving Hamilton's equations yields the impulse and spin changes of the individual bodies. We write them in a surprisingly compact form as appropriate derivatives of the eikonal phase obtained from the amplitude. It seems likely this structure persists to higher orders. We also point out various double-copy relations for general spin.

Phenomenology of nuclear scattering for a WIMP of arbitrary spin

We provide a first systematic and quantitative discussion of the phenomenology of the nonrelativistic effective Hamiltonian describing the nuclear scattering process for a weakly interacting massive particle (WIMP) of arbitrary spin ${j}_{\ensuremath{\chi}}$. To this aim we obtain constraints from a representative sample of present direct detection experiments assuming the WIMP-nucleus scattering process to be driven by each one of the 44 effective couplings that arise for ${j}_{\ensuremath{\chi}}\ensuremath{\le}2$. We find that a high value of the multipolarity $s\ensuremath{\le}2{j}_{\ensuremath{\chi}}$ of the coupling, related to the power of the momentum transfer $q$ appearing in the scattering amplitude, leads to a suppression of the expected rates and pushes the expected differential spectra to large recoil energies ${E}_{R}$. For $s\ensuremath{\le}4$ the effective scales probed by direct detection experiments can be suppressed by up to five orders of magnitude compared to the case of a standard spin-independent interaction. For operators with large $s$ the expected differential spectra can be pushed to recoil energies in the MeV range, with the largest part of the signal concentrated at ${E}_{R}\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{keV}$ and a peculiar structure of peaks and minima arising when both the nuclear target and the WIMPs are heavy. As a consequence the present bounds on the effective operators can be significantly improved by extending the recoil energy intervals to higher recoil energies. Our analysis assumes effective interaction operators that are irreducible under the rotation group. Such operators drive the interactions of high-multipole dark matter candidates, i.e., states that possess only the highest multipole allowed by their spin. As a consequence our analysis represents also the first phenomenological study of the direct detection of quadrupolar, octupolar, and hexadecapolar dark matter.

Effective theory of nuclear scattering for a WIMP of arbitrary spin

We introduce a systematic approach to characterize the most general non-relativistic WIMP-nucleus interaction allowed by Galilean invariance for a WIMP of arbitrary spin $j_\chi$ in the approximation of one-nucleon currents. Five nucleon currents arise from the nonrelativistic limit of the free nucleon Dirac bilinears. Our procedure consists in (1) organizing the WIMP currents according to the rank of the $2 j_\chi+1$ irreducible operator products of up to $2 j_\chi$ WIMP spin vectors, and (2) coupling each of the WIMP currents to each of the five nucleon currents. The transferred momentum $q$ appears to a power fixed by rotational invariance. For a WIMP of spin $j_\chi$ we find a basis of 4+20$j_\chi$ independent operators that exhaust all the possible operators that drive elastic WIMP-nucleus scattering in the approximation of one-nucleon currents. By comparing our operator basis, which is complete, to the operators already introduced in the literature we show that some of the latter for $j_\chi=1$ were not independent and some were missing. We provide explicit formulas for the squared scattering amplitudes in terms of the nuclear response functions, which are available in the literature for most of the targets used in WIMP direct detection experiments.

Causality constraints in large N QCD coupled to gravity

Confining gauge theories contain glueballs and mesons with arbitrary spin, and these particles become metastable at large $N$. However, metastable higher-spin particles, when coupled to gravity, are in conflict with causality. This tension can be avoided only if the gravitational interaction is accompanied by interactions involving other higher-spin states well below the Planck scale ${M}_{\mathrm{pl}}$. These higher-spin states can come from either the QCD sector or the gravity sector, but both these resolutions have some surprising implications. For example, QCD states can resolve the problem since there is a nontrivial mixing between the QCD sector and the gravity sector, requiring all particles to interact with glueballs at tree-level. If gravity sector states restore causality, any weakly coupled UV completion of the gravity sector must have many stringy features, with an upper bound on the string scale ${M}_{\text{string}}\ensuremath{\lesssim}\sqrt{{M}_{\mathrm{pl}}{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}/N}$, where ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$ is the confinement scale.

Fast Algorithms for General Spin Systems on Bipartite Expanders

A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism. The problem of approximating the partition function (the aggregate weight of spin assignments) or of sampling from the resulting probability distribution is typically intractable for general graphs. In this work, we consider arbitrary spin systems on bipartite expander Δ-regular graphs, including the canonical class of bipartite random Δ-regular graphs. We develop fast approximate sampling and counting algorithms for general spin systems whenever the degree and the spectral gap of the graph are sufficiently large. Roughly, this guarantees that the spin system is in the so-called low-temperature regime. Our approach generalises the techniques of Jenssen et al. and Chen et al. by showing that typical configurations on bipartite expanders correspond to “bicliques” of the spin system; then, using suitable polymer models, we show how to sample such configurations and approximate the partition function in Õ( n 2 ) time, where n is the size of the graph.

Quantum Heat Engines with Complex Working Media, Complete Otto Cycles and Heuristics.

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.

Inferring Nonlinear Many-Body Bell Inequalities From Average Two-Body Correlations: Systematic Approach for Arbitrary Spin- j Ensembles

Violating Bell's inequalities (BIs) allows one to certify the preparation of entangled states from minimal assumptions -- in a device-independent manner. Finding BIs tailored to many-body correlations as prepared in present-day quantum computers and simulators is however a highly challenging endeavour. In this work, we focus on BIs violated by very coarse-grain features of the system: two-body correlations averaged over all permutations of the parties. For two-outcomes measurements, specific BIs of this form have been theoretically and experimentally studied in the past, but it is practically impossible to explicitly test all such BIs. Data-driven methods -- reconstructing a violated BI from the data themselves -- have therefore been considered. Here, inspired by statistical physics, we develop a novel data-driven approach specifically tailored to such coarse-grain data. Our approach offers two main improvements over the existing literature: 1) it is directly designed for any number of outcomes and settings; 2) the obtained BIs are quadratic in the data, offering a fundamental scaling advantage for the precision required in experiments. This very flexible method, whose complexity does not scale with the system size, allows us to systematically improve over all previously-known Bell's inequalities robustly violated by ensembles of quantum spin-$1/2$; and to discover novel families of Bell's inequalities, tailored to spin-squeezed states and many-body spin singlets of arbitrary spin-$j$ ensembles.

The σ− Cohomology Analysis for Symmetric Higher-Spin Fields

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective σ− cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in AdS4. In the d-dimensional case Hp(σ−) is computed for any p and interpretation of Hp(σ−) is given both for the original Fronsdal system and for the associated systems of higher form fields.

Ground-state properties of a quantum frustrated spin chain with side spins and arbitrary spin s

The properties of the spin-s frustrated antiferromagnetic Heisenberg chain with side spins are studied by means of the coupled cluster method and the numerical exact diagonalization method. The results of the two methods both manifest that the ground state quantum phase diagram of the model consists of the Néel phase and the canted phase characterized by two pitch angles, irrespective of the value of the spin quantum number s. Although the phenomenon of quantum melting of magnetic long-range order is absent in the model, quantum fluctuation exerts an important influence on the property of the model. In addition to the reduction of magnetization, the nature of the phase transition from the Néel state to the canted state transforms from a classical second-order transition to a quantum first-order transition at any finite value of s. It is observed that the ways one of the two pitch angles evolves with frustration in quantum and classical cases, are qualitatively different in the large frustration parameter region. The location of the critical point and the physical quantities, including the ground state energy per spin and the magnetic order parameter, move toward their classical values in the form of power series in s.

Crossing symmetry in the planar limit

Crossing symmetry asserts that particles are indistinguishable from antiparticles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios in a scattering experiment are described by one and the same function. Why could we expect it to be true? In this work we examine this question in a simplified setup and take steps towards illuminating a possible physical interpretation of crossing symmetry. To be more concrete, we consider planar scattering amplitudes involving any number of particles with arbitrary spins and masses to all loop orders in perturbation theory. We show that by deformations of the external momenta one can smoothly interpolate between pairs of crossing channels without encountering singularities or violating mass-shell conditions and momentum conservation. The analytic continuation can be realized using two types of moves. The first one makes use of an $iϵ$ prescription for avoiding singularities near the physical kinematics and allows us to adjust the momenta of the external particles relative to one another within their light cones. The second, more violent, step involves a rotation of subsets of particle momenta via their complexified light cones from the future to the past and vice versa. We show that any singularity along such a deformation would have to correspond to two beams of particles scattering off each other. For planar Feynman diagrams, these kinds of singularities are absent because of the particular flow of energies through their propagators. We prescribe a five-step sequence of such moves that combined together proves crossing symmetry for planar scattering amplitudes in perturbation theory, paving a way towards settling this question for more general scattering processes in quantum field theories.