Arbitrary Spin Research Articles

Analytical Black-Hole Binary Merger Waveforms

We present a highly accurate, fully analytical model for the late inspiral, merger, and ringdown of black-hole binaries with arbitrary mass ratios and spin vectors and the associated gravitational radiation, including the contributions of harmonics beyond the fundamental mode. This model assumes only that nonlinear effects remain small throughout the entire coalescence and is developed based on a physical understanding of the dynamics of late stage binary evolution, in particular, on the tendency of the dynamical binary spacetime to behave like a linear perturbation of the stationary merger-remnant spacetime, even at times before the merger has occurred. We demonstrate that our model agrees with the most accurate numerical relativity results to within their own uncertainties throughout the merger-ringdown phase, and it does so for example cases spanning the full range of binary parameter space that is currently testable with numerical relativity. Furthermore, our model maintains accuracy back to the innermost stable circular orbit of the merger-remnant spacetime over much of the relevant parameter space, greatly decreasing the need to introduce phenomenological degrees of freedom to describe the late inspiral.

Single-Shot Holographic Compression from the Area Law.

The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. We show that, for any state that fulfills an area law, the reduced quantum state of a region of space can be unitarily compressed into a thickened boundary of the region. If the interior of the region is lost after this compression, the full quantum state can be recovered to high precision by a quantum channel only acting on the thickened boundary. The thickness of the boundary scales inversely proportional to the error for arbitrary spin systems and logarithmically with the error for quasifree bosonic systems. Our results can be interpreted as a single-shot operational interpretation of the area law. The result for spin systems follows from a simple inequality showing that any probability distribution with entropy S can be approximated to error ϵ by a distribution with support of size exp(S/ϵ), which we believe to be of independent interest. We also discuss an emergent approximate correspondence between bulk and boundary operators and the relation of our results to tensor network states.

Symmetries of Hamiltonians describing systems with arbitrary spins

We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial relationships between the operator invariants, or equivalently, between eigenvalues of those invariants.

Quasiperiodic magnetic chain as a spin filter for arbitrary spin states

We show that a quasiperiodic magnetic chain comprising magnetic atomic sites sequenced in Fibonacci pattern can act as a prospective candidate for spin filters for particles with arbitrary spin states. This can be achieved by tuning a suitable correlation between the amplitude of the substrate magnetic field and the on-site potential of the magnetic sites, which can be controlled by an external gate voltage. Such correlation leads to a spin filtering effect in the system, allowing one of the spin components to completely pass through the system while blocking the others over the allowed range of energies. The underlying mechanism behind this phenomena holds true for particles with any arbitrary spin states S = 1, 3/2, 2, . . ., in addition to the canonical case of spin-half particles. Our results open up the interesting possibility of designing a spin demultiplexer using a simple quasiperiodic magnetic chain system. Experimental realization of this theoretical study might be possible by using ultracold quantum gases, and can be useful in engineering new spintronic devices.

Spin-polarized localization in a magnetized chain

We investigate a simple tight-binding Hamiltonian to understand the stability of spin-polarized transport of states with an arbitrary spin content in the presence of disorder. The general spin state is made to pass through a linear chain of magnetic atoms, and the localization lengths are computed. Depending on the value of spin, the chain of magnetic atoms unravels a hidden transverse dimensionality that can be exploited to engineer energy regimes where only a selected spin state is allowed to retain large localization lengths. We carry out a numerical anmalysis to understand the roles played by the spin projections in different energy regimes of the spectrum. For this purpose, we introduce a new measure, dubbed spin-resolved localization length. We study uncorrelated disorder in the potential profile offered by the magnetic substrate or in the orientations of the magnetic moments concerning a given direction in space. Our results show that the spin filtering effect is robust against weak disorder and hence the proposed system should be a good candidate model for experimental realizations of spin-selective transport devices.

Covariant equations of motion of extended bodies with arbitrary mass and spin multipoles

This paper employs the post-Newtonian approximations of scalar-tensor theory of gravity along with the Cartesian STF tensors and the Blanchet-Damour multipole formalism to derive translational and rotational equations of motion of N extended bodies with arbitrary distribution of mass and velocity. We assume that spacetime can be covered by a global coordinate chart which is Minkowskian at infinity. We also introduce N local coordinate charts adapted to each body and covering a finite domain of space around the body. Gravitational field of each body is parametrized by an infinite set of the body's mass and spin multipoles and tidal multipoles of external N-1 bodies. The origin of the local coordinates is set moving along accelerated worldline of the center of mass of the body by an appropriate choice of the internal and external dipole moments of its gravitational field. Translational and rotational equations of motion are derived by integrating microscopic equations of matter and applying the method of asymptotic matching. The matching is also used for separating the post-Newtonian self-field effects from the external gravitational environment and for constructing the effective background spacetime manifold. It allows us to present the equations of translational and rotational motion of each body in covariant form by making use of the Einstein principle of equivalence. Our approach significantly generalizes the Mathisson-Papapetrou-Dixon covariant equations of motion with regard to the number of body's multipoles and the post-Newtonian terms taken into account. The equations of translational and rotational motion derived in the present paper include the infinite set of mass and spin multipoles of the bodies and can be used for much more accurate prediction of orbital dynamics of extended bodies in inspiraling binary systems before they merge.

Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering

We provide universal expressions for the classical piece of the amplitude given by the graviton/photon exchange between massive particles of arbitrary spin, at both tree and one loop level. In the gravitational case this leads to higher order terms in the post-Newtonian expansion, which have been previously used in the binary inspiral problem. The expressions are obtained in terms of a contour integral that computes the Leading Singularity, which was recently shown to encode the relevant information up to one loop. The classical limit is performed along a holomorphic trajectory in the space of kinematics, such that the leading order is enough to extract arbitrarily high multipole corrections. These multipole interactions are given in terms of a recently proposed representation for massive particles of any spin by Arkani-Hamed et al. This explicitly shows universality of the multipole interactions in the effective potential with respect to the spin of the scattered particles. We perform the explicit match to standard EFT operators for S = frac{1}{2} and S = 1. As a natural byproduct we obtain the classical pieces up to one loop for the bending of light.

The simplest massive S-matrix: from minimal coupling to black holes

In this paper, we explore the physics of electromagnetically and gravitationally coupled massive higher spin states from the on-shell point of view. Starting with the three-point amplitude, we focus on the simplest amplitude characterized by matching to minimal coupling in the UV. In the IR, for charged states this leads to g = 2 for arbitrary spin, and the leading deformation corresponds to the anomalous magnetic dipole moment. We proceed to construct the (gravitational) Compton amplitude for generic spins via consistent factorization. We find that in gravitation couplings, the leading deformation leads to inconsistent factorization. This implies that for systems with Gauge2 = Gravity relations, such as perturbative string theory, all charged states must have g = 2. It is then natural to ask for generic spin, what is the theory that yields such minimal coupling. By matching to the one body effective action, we verify that for large spins the answer is Kerr black holes. This identification is then an on-shell avatar of the no- hair theorem. Finally using this identification as well as the newly constructed Compton amplitudes, we proceed to compute the spin-dependent pieces for the classical potential at 2PM order up to degree four in spin operator of either black holes.

Black holes and binary mergers in scalar Gauss-Bonnet gravity: Scalar field dynamics

We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss--Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then study the evolution of nonspinning black-hole binaries with various mass ratios and produce the first scalar waveform for a coalescence. An estimate of the energy loss in scalar radiation and the effect this has on orbital dynamics and the phase of the GWs (entering at quadratic order in the coupling) show that GW detections can set the most stringent constraint to date on theories that exhibit a coupling between a scalar field and the Gauss--Bonnet invariant.

A Haptic Model for the Quantum Phase of Fermions and Bosons in Hilbert Space Based on Knot Theory

A generalization of the famous Dirac belt trick opens up the way to a haptic model for quantum phases of fermions and bosons in Hilbert space based on knot theory. We introduce a simple paper strip model as an aid for visualization of the quantum phases before and after Hopf-mapping, which can be extended to arbitrary spin states with almost no mathematical formalism. Knot theory arises naturally, leading to the Jones polynomials derived from Artin’s braid group for fermionic knots and for bosonic links. The paper strip model explicitly illuminates the relation between these knots and links within the S U ( 2 ) -representation of spin-jstates in C 2 j + 1 before Hopf-mapping and the number p = 2 j of nodes in the stellar representation in C P 1 after Hopf mapping.

Two-Electron-Spin Ratchets as a Platform for Microwave-Free Dynamic Nuclear Polarization of Arbitrary Material Targets.

Optically pumped color centers in semiconductor powders can potentially induce high levels of nuclear spin polarization in surrounding solids or fluids at or near ambient conditions, but complications stemming from the random orientation of the particles and the presence of unpolarized paramagnetic defects hinder the flow of polarization beyond the defect's host material. Here, we theoretically study the spin dynamics of interacting nitrogen-vacancy (NV) and substitutional nitrogen (P1) centers in diamond to show that outside protons spin-polarize efficiently upon a magnetic field sweep across the NV-P1 level anticrossing. The process can be interpreted in terms of an NV-P1 spin ratchet, whose handedness, and hence the sign of the resulting nuclear polarization, depends on the relative timing of the optical excitation pulse. Further, we find that the polarization transfer mechanism is robust to NV misalignment relative to the external magnetic field, and efficient over a broad range of electron-electron and electron-nuclear spin couplings, even if proxy spins feature short coherence or spin-lattice relaxation times. Therefore, these results pave the route toward the dynamic nuclear polarization of arbitrary spin targets brought in proximity with a diamond powder under ambient conditions.

Ultrafast Spin Initialization in a Gated InSb Nanowire Quantum Dot

We propose a fast and accurate spin initialization method for a single electron trapped in an electrostatic quantum dot. The dot is created in a nanodevice composed of a catalytically grown indium antimonide (InSb) nanowire and nearby gates to which control voltages are applied. Initially we insert a single electron of arbitrary spin into the wire. Operations on spin are performed using the Rashba spin-orbit interaction induced by an electric field. First, a single pulse of voltages applied to lateral gates is used to split the electron wavepacket into two parts with opposite spin orientations. Next, another voltage pulse applied to the remaining gates rotates spins of both parts in opposite directions by $\pi/2$. This way, initially opposite spin parts eventually point in the same direction, along the axis of the quantum wire. We thus set spin in a predefined direction regardless of its initial orientation. This is achieved in time less than $60\,\mathrm{ps}$ without the use of microwaves, photons or external magnetic fields.

Massive scattering amplitudes in six dimensions

We show that a natural spinor-helicity formalism that can describe massive scattering amplitudes exists in D = 6 dimensions. This is arranged by having helicity spinors carry an index in the Dirac spinor 4 of the massive little group, SO(5) ∼ Sp(4). In the high energy limit, two separate kinds of massless helicity spinors emerge as required for consistency with arXiv:0902.0981, with indices in the two SU(2)’s of the massless little group SO(4). The tensors of 4 lead to particles with arbitrary spin, and using these and demanding consistent factorization, we can fix 3− and 4-point tree amplitudes of arbitrary masses and spins: we provide examples. We discuss the high energy limit of scattering amplitudes and the Higgs mechanism in this language, and make some preliminary observations about massive BCFW recursion.

Chiral vortical effect for an arbitrary spin

The spin Hall effect of light attracted enormous attention in the literature due to the ongoing progress in developing of new optically active materials and metamaterials with non-trivial spin-orbit interaction. Recently, it was shown that rotating fermionic systems with relativistic massless spectrum may exhibit a 3-dimensional analogue of the spin Hall current — the chiral vortical effect (CVE). Here we show that CVE is a general feature of massless particles with an arbitrary spin. We derive the semi-classical equations of motion in rotating frame from the first principles and show how by coordinate transformation in the phase space it can be brought to the intuitive form proposed in [1]. Our finding clarifies the superficial discrepancies in different formulations of the chiral kinetic theory for rotating systems. We then generalize the chiral kinetic theory, originally introduced for fermions, to an arbitrary spin and study chirality current in a general rotating chiral medium. We stress that the higher-spin realizations of CVE can be in principle observed in various setups including table-top experiments on quantum optics.

Energy spectra of a spin- XY spin molecule interacting with a single mode field cavity

We report results from our continued investigations on a finite-size chain (molecule) of L spin- spins with XY spin exchange interaction coupled at an arbitrary spin site to a single mode of an electromagnetic field via the Jaynes-Cummings model. Here we study the energy spectra in the case of an arbitrary photon fill number n, as compared to the n = 1 limit in our previous work [J. Phys.: Conf. Ser. 682 (2016) 012032] and [J. Phys.: Conf. Ser. 764 (2016) 012017]. By building the appropriate combinations of basis product states involving the photon as well as the up down spins it is possible to simplify the systems that are necessary to diagonalize from n × 2L to at most 2L . This results are in tune with those reported in the recent paper by N. Wu [Phys. Rev. B 97 (2018) 014301], and may prove to be useful for the quantum computing aficionados.

Pauli-based fermionic teleportation with free massive particles by electron-exchange collisions

Fundamental non-locality in quantum mechanical scattering processes is investigated by means of Fermionic teleportation. Our scenario employs free massive particles, electrons and atoms, within a twofold electron-exchange collision approach whereby, in the first collision, also generating the necessary spin–spin entanglement between initially unpolarized electrons and atoms. It is shown that in a second collision an arbitrary spin polarization state of a free electron can be teleported onto the other electron which has never been in contact with the first one. The underlying scheme relies on and is a direct consequence of the Pauli-principle and makes use of a high symmetry in spin space thereby avoiding restoration of the teleported states. The scattering process (teleportation) is highly symmetric allowing for interchanging the electronic and atomic constituents without loss of generality. Re-interpretation of Li and Na data reveals the feasibility and capability of Fermionic teleportation demonstrated by numerical and experimental data for the teleportation fidelity.

Spin splittings from first-order symmetry-adapted perturbation theory without single-exchange approximation.

The recently proposed spin-flip symmetry-adapted perturbation theory (SF-SAPT) first-order exchange energy [Patkowski et al., J. Chem. Phys. 148, 164110 (2018)] enables the standard open-shell SAPT approach to treat arbitrary spin states of the weakly interacting complex. Here, we further extend first-order SF-SAPT beyond the single-exchange approximation to a complete treatment of the exchanges of electrons between monomers. This new form of the exchange correction replaces the single-exchange approximation with a more moderate single-spin-flip approximation. The newly developed expressions are applied to a number of small test systems to elucidate the quality of both approximations. They are also applied to the singlet-triplet splittings in pancake bonded dimers. The accuracy of the single-exchange approximation deteriorates at short intermolecular separations, especially for systems with few electrons and for the high-spin state of the complex. In contrast, the single-spin-flip approximation is exact for interactions involving a doublet molecule and remains highly accurate for any number of unpaired electrons. Because the single-exchange approximation affects the high-spin and low-spin states of pancake bonded complexes evenly, the resulting splitting values are of similar accuracy to those produced by the formally more accurate single-spin-flip approximation.

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models

Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g. the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na2IrO3 and alpha-RuCl3. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary spin patterns in the cluster ground states obtained by exact diagonalization. Global trends in the phase diagram are understood in combination with the analytical mappings of the Hamiltonian that uncover peculiar links to known models - Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice - or reveal entire manifolds of exact fluctuation-free ground states. Finally, our study can serve as a methodological example that can be applied to other spin models with complex bond-dependent non-Heisenberg interactions.

Ising Model: Local Spin Correlations and Conformal Invariance

We study the 2-dimensional Ising model at critical temperature on a simply connected subset {Omega_{delta}} of the square grid {deltamathbb{Z}^{2}}. The scaling limit of the critical Ising model is conjectured to be described by Conformal Field Theory; in particular, there is expected to be a precise correspondence between local lattice fields of the Ising model and the local fields of Conformal Field Theory. Towards the proof of this correspondence, we analyze arbitrary spin pattern probabilities (probabilities of finite spin configurations occurring at the origin), explicitly obtain their infinite-volume limits, and prove their conformal covariance at the first (non-trivial) order. We formulate these probabilities in terms of discrete fermionic observables, enabling the study of their scaling limits. This generalizes results of Hongler (Conformal invariance of Ising model correlations. Ph.D. thesis, [Hon10]), Hongler and Smirnov (Acta Math 211(2):191–225, [HoSm13]), Chelkak, Hongler, and Izyurov (Ann. Math. 181(3), 1087–1138, [CHI15]) to one-point functions of any local spin correlations. We introduce a collection of tools which allow one to exactly and explicitly translate any spin pattern probability (and hence any lattice local field correlation) in terms of discrete complex analysis quantities. The proof requires working with multipoint lattice spinors with monodromy (including construction of explicit formulae in the full plane), and refined analysis near their source points to prove convergence to the appropriate continuous conformally covariant functions.

Exact renormalization group for quantum spin systems

We show that the diagrammatic approach to quantum spin systems developed in a seminal work by Vaks, Larkin, and Pikin [Sov. Phys. JETP 26, 188 (1968)] can be embedded in the framework of the functional renormalization group. The crucial insight is that the generating functional of the time-ordered connected spin correlation functions of an arbitrary quantum spin system satisfies an exact renormalization group flow equation which resembles the corresponding flow equation of a system of interacting bosons. The $SU (2)$ spin algebra is implemented via a non-trivial initial condition for the renormalization group flow. Our method is rather general and offers a new non-perturbative approach to quantum spin systems.