Large Spin Values Research Articles

Two-loop five-point integrals: light, heavy and large-spin correlators

We evaluated all two-loop conformal integrals appearing in five-point correlation functions of protected operators of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Super Yang-Mills in several kinematical regimes. Starting from the correlation function of the lightest operators of the theory, we were able to extract structure constants of up to two spinning operators for small and large values of spin and the tensor structure label (polarization). We conjectured an universal all-loop behaviour for the large-spin, small-polarization structure constants and comment on the subtleties of analytically continuing it from finite to large spin. We also consider correlation functions of heavier operators that get factorized in the more fundamental object called decagon. We fixed this object at two loops in general kinematics and studied its physical properties under OPE and null limits.

Magnetic phase diagrams and large magnetocaloric effects of the two-dimensional antiferromagnetic triangular lattice of Gd3+ ions in KBaGd(BO3)2

We report a detailed study of the magnetic properties of KBaGd(BO$_3$)$_2$, in which magnetic Gd$^{3+}$ ($S=7/2$) ions form into two-dimensional triangular layers. Magnetization, specific heat and magnetocaloric effect (MCE) measurements have been performed on KBaGd(BO$_3$)$_2$ single crystals. The results show that a long-range antiferromagnetic state is established below $T_{\rm N}=0.24$ K. In zero fields, only about half of the full entropy is released at $T_{\rm N}$, indicating that not all the magnetic moments are frozen below the ordering temperature, as expected from the geometrical frustration of the triangular spin lattice. Further studies under external fields were performed down to 50 mK, and the magnetic phase diagrams are established with magnetic fields applied both within and perpendicular to the triangular plane. KBaGd(BO$_3$)$_2$ serves as an example of a two-dimensional triangular lattice with large spin values ($S=7/2$) and can be directly compared with the iso-structure KBaR(BO$_3$)$_2$ (R = Dy-Yb) family of doublet ground states, which exhibit effective spins of $S=1/2$.

Electronic and magnetic properties of metal–organic polymers with 4d and 5d-transition metal ions

The electronic and magnetic properties of one-dimensional polymers of zwitterionic quinone (ZQ) molecules with 4d and 5d transition metals (TM) are studied using density functional calculations. We present the results of first-principle calculations for the electronic and magnetic properties, including the magnetic anisotropy energy (MAE) of selected 4d- and 5d-ZQ polymers, using the Vienna Ab-initio Simulation Package (VASP). In particular, a pronounced magnetic character is found for TM-ZQ polymers with the TM ions Mo, Ru, Rh, Ag, Re, and Ir, having local magnetic moments between 1 and 4 μB and ferromagnetic or antiferromagnetic nearest neighbor exchanges. The large values of spin–orbit coupling lead to high magnetic anisotropy energies (MAE) especially for Rh-ZQ and Re-ZQ, exceeding the MAE of its 3d counterparts considerably. All investigated TM-ZQ polymer chains were found to be spin-polarized semiconductors, which make them, together with the high MAE, excellent candidate materials for spintronics.

Time-dependent spintronic anisotropy in magnetic molecules

We theoretically study the quench dynamics of induced anisotropy of a large-spin magnetic molecule coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework, which takes into account all correlations in very accurate manner. We determine the system's response to a quench in the spin-dependent coupling to ferromagnetic leads. In particular, we focus on the transient dynamics associated with crossing from the weak to the strong coupling regime, where the Kondo correlations become important. The dynamics is examined by calculating the time-dependent expectation values of the spin-quadrupole moment and the associated spin operators. We identify the relevant time scales describing the quench dynamics and determine the influence of the molecule's effective exchange coupling and leads spin-polarization on the dynamical behavior of the system. Furthermore, the generalization of our predictions for large values of molecule's spin is considered. Finally, we analyze the effect of finite temperature and show that it gives rise to a reduction of magnetic anisotropy by strong suppression of the time-dependent spin-quadrupole moment due to thermal fluctuations.

Faithful analytical effective-one-body waveform model for spin-aligned, moderately eccentric, coalescing black hole binaries

We present a new effective-one-body (EOB) model for eccentric binary coalescences. The model stems from the state-of-the-art model TEOBiResumS_SM for circularized coalescing black-hole binaries, that is modified to explicitly incorporate eccentricity effects both in the radiation reaction and in the waveform. Using Regge-Wheeler-Zerilli-type calculations of the gravitational wave losses as benchmarks, we find that a rather accurate ($\ensuremath{\sim}1%$) expression for the radiation reaction along mildly eccentric orbits ($e\ensuremath{\sim}0.3$) is given by dressing the current, EOB-resummed, circularized angular momentum flux, with a leading-order (Newtonian-like) prefactor valid along general orbits. An analogous approach is implemented for the waveform multipoles. The model is then completed by the usual merger-ringdown part informed by circularized numerical relativity (NR) simulations. The model is validated against the 22, publicly available, NR simulations calculated by the Simulating eXtreme Spacetime (SXS) Collaboration, with mild eccentricities, mass ratios between 1 and 3, and up to rather large dimensionless spin values ($\ifmmode\pm\else\textpm\fi{}0.7$). The maximum EOB/NR unfaithfulness, calculated with Advanced LIGO noise, is at most of order 3%. The analytical framework presented here should be seen as a promising starting point for developing highly faithful waveform templates driven by eccentric dynamics for present, and possibly future, gravitational wave detectors.

On Spin dependence of the Fundamental Plane of black hole activity

ABSTRACT The Fundamental Plane (FP) of black hole (BH) activity in galactic nuclei relates X-ray and radio luminosities to BH mass and accretion rate. However, there is a large scatter exhibited by the data, which motivated us for a new variable. We add BH spin as a new variable and estimate the spin dependence of the jet power and disc luminosity in terms of radio and X-ray luminosities. We assume the Blandford–Znajek process as the main source of the outflow, and find that the jet power depends on BH spin stronger than quadratically at moderate and large spin values. We perform a statistical analysis for 10 active galactic nuclei (AGNs) which have sub-Eddington accretion rates and whose spin values are measured independently via the reflection or continuum-fitting methods, and find that the spin-dependent relation describes the data significantly better. This analysis, if supported with more data, could imply not only the spin dependence of the FP relation, but also the Blandford–Znajek process in AGN jets.

Hybridization and Decay of Magnetic Excitations in Two-Dimensional Triangular Lattice Antiferromagnets

Elementary quasiparticles in solids such as phonons and magnons occasionally have nontrivial interactions between them, as well as among themselves. As a result, their energy eigenvalues are renormalized, the quasiparticles spontaneously decay into a multi-particle continuum state, or they are hybridized with each other when their energies are close. As discussed in this review, such anomalous features can appear dominantly in quantum magnets but are not, a priori, negligible for magnetic systems with larger spin values and noncollinear magnetic structures. We review the unconventional magnetic excitations in two-dimensional triangular lattice antiferromagnets and discuss their implications on related issues.

Quantum coherence recovery through Stern–Gerlach erasure

Quantum erasure probes the dynamic nature of quantum coherence. It allows quantum systems to exhibit interference effects by recovering coherence that was previously lost through entanglement with another system. In this paper we examine the concept of a quantum eraser which creates and then erases path information through repeated use of the Stern–Gerlach effect. We explore the degree to which this eraser can recover quantum coherence. We find that the recovered coherence depends on the spin of the objects passing through the eraser and on the relative angle between the orientations of the eraser’s two magnets. We determine that full coherence can always be recovered for spin-1/2 objects independent of the value of the spin projection but cannot always be recovered for objects with larger spin values. We then discuss how the quantum coherence could be experimentally measured in this setup. Finally, we comment on the limitations of this Stern–Gerlach eraser and similar erasure schemes.

Physics of integer-spin antiferromagnetic chains: Haldane gaps and edge states

The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg chain. We discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We next study the robustness of the edge states of the spin one chain by studying by the DMRG algorithm a spin one ladder. We show that the peculiar hidden topological order of the spin one chain disappears smoothly by increasing the ladder rung coupling without any intervening phase transition. This is evidence for the fragile character of the topological order of the spin one chain.

Giant Heterometallic [Mn36Ni4]0/2- and [Mn32Co8] "Loops-of-Loops-and-Supertetrahedra" Molecular Aggregates.

We report the synthesis, crystal structures and magnetic properties of the giant heterometallic [Mn36Ni4]2−/0 (compounds 1, 2)/[Mn32Co8] (compound 3) “loops-of-loops-and-supertetrahedra” molecular aggregates and of a [Mn2Ni6]2+ compound (cation of 4) that is structurally related with the cation co-crystallizing with the anion of 1. In particular, after the initial preparation and characterization of compound [Mn2Ni6(μ4-O)2(μ3-OH)3(μ3-Cl)3(O2CCH3)6(py)8]2+[Mn36Ni4(μ4-O)8(μ3-O)4(μ3-Cl)8Cl4(O2CCH3)26(pd)24(py)4]2− (1) we targeted the isolation of (i) both the cationic and the anionic aggregates of 1 in a discrete form and (ii) the Mn/Co analog of [Mn36Ni4]2− aggregate. Our synthetic efforts toward these directions afforded the discrete [Mn36Ni4] “loops-of-loops-and-supertetrahedra” aggregate [Mn36Ni4(μ4-O)8(μ3-O)4(μ3-Cl)8Cl2(O2CCH3)26(pd)24(py)4(H2O)2] (2), the heterometallic Mn/Co analog [Mn32Co8(μ4-O)8(μ3-O)4(μ3-Cl)8Cl2(μ2-OCH2CH3)2(O2CCH3)28(pd)22(py)6] (3) and the discrete [Mn2Ni6]2+ cation [Mn2Ni6(μ4-O)2(μ3-OH)4(μ3-Cl)2(O2CCH3)6(py)8](ClO4)(OH) (4). The structure of 1 consists of a mixed valence []2− molecular aggregate that contains two loops separated by two supertetrahedral units and a []2+ cation based on two [MnIII(μ4-O)(μ3-OH)1.5(μ3-Cl)1.5]4+ cubane sub-units connected through both mono- and tri-atomic bridges provided by the μ4-O2− and carboxylate anions. The structures of 2–4 are related to those of the compounds co-crystallized in 1 exhibiting however some differences that shall be discussed in detail in the manuscript. Magnetism studies revealed the presence of dominant ferromagnetic interactions in 1–3 that lead to large ground state spin (ST) values for the “loops-of-loops-and-supertetrahedra” aggregates and antiferromagnetic exchange interactions in 4 that lead to a low (and possibly zero) ST value. In particular, dc and ac magnetic susceptibility studies revealed that the discrete [Mn36Ni4] aggregate exhibits a large ST value ~ 26 but is not a new SMM. The ac magnetic susceptibility studies of the [Mn32Co8] analog revealed an extremely weak beginning of an out-of-phase tail indicating the presence of a very small relaxation barrier assignable to the anisotropic Co2+ions and a resulting out-of-phase ac signal whose peak is at very low T.

Periastron shift for a spinning test particle around naked singularities

In the present article, we investigate the Periastron precession for a spinning test particle moving in nearly circular orbits around naked singularities. We consider two well-known solutions that can produce a spacetime with naked singularity---(a) first, the Reissner-Nordstr\om metric, which is a static charged solution with spherical symmetry, and (b) second, the stationary, axisymmetric Kerr metric. For simplicity, we only consider the motion confined on the equatorial plane in both these cases and solve exactly the Mathisson-Papapetrou equations. In addition, we analytically compute the Periastron precession within the framework of linear spin approximation. The inclusion of the spin parameter modifies the results with nonspinning particles and also reflects some interesting properties of the naked geometries. Furthermore, we carried out a numerical approach without any assumptions to probe the large order spin values. The implication of the spin-curvature coupling in connection with the naked geometries is also discussed.

Spin states of electrons in quantum dots upon heating. Simulation by the Feynman path integral method. Magnetic properties

Temperature dependences of spin states and spin paramagnetic susceptibility in ellipsoidal quantum dots (QDs) containing two or three electrons are numerically simulated using ab initio calculations based on the Feynman path integral method. Limits of the thermal stability of spin states are estimated. Upon cooling, the pairing of spins of an electron pair is most intense in spherical QDs; notably, prolate QDs hinder the pairing more strongly than the oblate ones. When the spherical shape of a QD is distorted, a characteristic peak in the temperature dependence of the electron-pair magnetic susceptibility shifts to lower temperatures. A spin of the system of three electrons may either increase or decrease upon cooling, depending on the QD shape. In the case of three electrons, strong spatial anisotropy of the electron-confining field causes a relative decrease in the energy of states with large spin values.

Entanglement for a Two-Level Atomic System Interacting with Two-Mode Spin States

A key element in the architecture of quantum information processing is a reliable physical interface between fields and qubits. Here, we study the population transfer and entanglement for a two-level atomic system interacting with entangled spin coherent states (ESCSs) considering one- and two-mode interactions. The results show that decrease in the spin number provides a periodic behavior of the entanglement exhibiting the sudden death and birth phenomena. For large values of spin, the atom–field system stabilizes at high value of entanglement during the time evolution exhibiting maximum correlations for both cases of one- and two-mode interactions. Finally, we find an interesting correlation between the entanglement and the population transfer during the time evolution. In particular, we show that the population may be used as an indicator of nonlocal correlations in the system under consideration.

Magnetic properties of a classical XY spin dimer in a “planar” magnetic field

Single-molecule magnetism originates from the strong intra-molecular magnetic coupling of a small number of interacting spins. Such spins generally interact very weakly with the neighboring spins in the other molecules of the compound, therefore, inter-molecular spin couplings are negligible. In certain cases the number of magnetically coupled spins is as small as a dimer, a system that can be considered the smallest nanomagnet capable of storing non-trivial magnetic information on the molecular level. Additional interesting patterns arise if the spin motion is confined to a two-dimensional space. In such a scenario, clusters consisting of spins with large-spin values are particularly attractive since their magnetic interactions can be described well in terms of classical Heisenberg XY spins. In this work we calculate exactly the magnetic properties of a nanomagnetic dimer of classical XY spins in a “planar” external magnetic field. The problem is solved by employing a mathematical approach whose idea is the introduction of auxiliary spin variables into the starting expression of the partition function. Results for the total internal energy, total magnetic moment, spin–spin correlation function and zero-field magnetic susceptibility can serve as a basis to understand the magnetic properties of large-spin dimer building blocks.

Analysis of Dissociation—Recombination Processes for the CO2 Molecule with the Spin—Orbit Coupling Taken into Account

The dissociation CO2(X 1Σ) + M → CO(X 1Σ) + O(3P) + M and recombination CO(X 1Σ) + O(3P) + M → CO2(X 1Σ) + M processes are considered with the spin—orbit coupling taken into account in the ground and several excited states of the CO2 molecule. Because of the specific features of mutual position of potential energy surfaces of the CO2 molecule in the ground and several excited states and the large values of spin—orbit interaction matrix elements, which causes the quantum nonadiabatic transition of the molecule from one state to another, these processes become effectively spin-allowed and the rate constants for the nonadiabatic reactions have large values. The proposed dissociation and recombination mechanisms include reactions involving singlet—triplet crossings.

Order and excitations inlarge−Skagome-lattice antiferromagnets

We systematically investigate the ground-state and the spectral properties of antiferromagnets on a kagom\'{e} lattice with several common types of the planar anisotropy: $XXZ$, single-ion, and out-of-plane Dzyaloshinskii-Moriya. Our main focus is on the role of nonlinear, anharmonic terms, which are responsible for the quantum order-by-disorder effect and for the corresponding selection of the ground-state spin structure in many of these models. The $XXZ$ and the single-ion anisotropy models exhibit a quantum phase transition between the ${\bf q}\!=\!0$ and the $\sqrt{3}\times\!\sqrt{3}$ states as a function of the anisotropy parameter, offering a rare example of the quantum order-by-disorder fluctuations favoring a ground state which is different from the one selected by thermal fluctuations. The nonlinear terms are also shown to be crucial for a very strong near-resonant decay phenomenon leading to the quasiparticle breakdown in the kagom\'{e}-lattice antiferromagnets whose spectra are featuring flat or weakly dispersive modes. The effect is shown to persist even in the limit of large spin values and should be common to other frustrated magnets with flat branches of excitations. Model calculations of the spectrum of the $S=5/2$ Fe-jarosite with Dzyaloshinskii-Moriya anisotropy provide a convincing and detailed characterization of the proposed scenario.

Spectrum of the excitedN*andΔ*baryons in a relativistic chiral quark model

The spectrum of the SU(2) flavor baryons is studied in the frame of a relativistic chiral quark potential model based on the one-pion and one-gluon exchange mechanisms. It is argued that the ${N}^{*}$ and ${\mathrm{\ensuremath{\Delta}}}^{*}$ resonances strongly coupled to the $\ensuremath{\pi}N$ channel are identified with the orbital configurations $(1{S}_{1/2}{)}^{2}(nlj)$ with a single valence quark in the excited state ($nlj$). With the obtained selection rules based on the ``chiral constraint,'' we show that it is possible to construct a schematic periodic table of baryon resonances, consistent with the experimental data and yielding no ``missing resonances.'' A new original method for the treatment of the center of mass problem is suggested which is based on the separation of the three-quark Dirac Hamiltonian into the parts, corresponding to the Jacobi coordinates. The numerical estimations for the energy positions of the nucleon and delta baryons (up to and including F-wave ${N}^{*}$ and ${\mathrm{\ensuremath{\Delta}}}^{*}$ resonances), obtained within the field-theoretical framework by using time ordered perturbation theory, yield an overall good description of the experimental data at the level of the relativized constituent quark model of S. Capstick and W. Roberts without any fitting parameters. The only free parameter of the linear confinement potential was fitted previously by Th. Gutsche to reproduce the axial charge of the nucleon. The ground state $\mathrm{\ensuremath{\Delta}}(1232)$ is well reproduced. However, nucleon ground state and most of the radially excited baryon resonances (including Roper) are overestimated. On the contrary, the first band of the orbitally excited baryon resonances with a negative parity are underestimated. At the same time, the second band of the orbitally excited ${\mathrm{\ensuremath{\Delta}}}^{*}$ states with the negative parity are mostly overestimated, while the ${N}^{*}$ states are close to the experimental boxes. The theoretical estimations of the energy levels for the positive parity baryon resonances with $\mathrm{J}=5/2$, $7/2$ are close to the experimental data. At higher energies, where the experimental data are poor, we can extend our model schematically and predict an existence of seven ${N}^{*}$ and four ${\mathrm{\ensuremath{\Delta}}}^{*}$ new states with larger spin values.

Theoretical studies on {3d-Gd} and {3d-Gd-3d} complexes: Effect of metal substitution on the effective exchange interaction

Series of DFT calculations on [L1Ni(H2O)2Gd(NO3)3] (1) and their transition metal substituted models {CrIIIGdIII}, {FeIIGdIII}, {MnIIGdIII} and {CuIIGdIII} have been performed to probe the electronic effects of the metal substitution on the sign and strength of magnetic coupling. Our results unfold an interesting observation that the strength of the exchange is related to the d-orbital occupancy with occupancy on the eg orbitals resulting in stronger ferromagnetic exchange while progressively filling the t2g orbitals leads to a reduction in the computed J values. Further, we extend our studies to the trinuclear {3d-Ln-3d} [L2M2Ln][ClO4] (LH3=(S)P[N(Me)N=CH-C6H3-2-OH-3-OMe]3) (here M=Cu2+, Ni2+ and Mn2+ and Ln=GdIII and LaIII) complexes possessing phosphorus, salicylideneaminooxy and Schiff base supported ligands to corroborate our findings in dinuclear models. By computing the nearest neighbor and next-nearest neighbor interactions in all three complexes, our studies reveal that the observation of strong exchange with eg occupancy is preserved also in the trinuclear complexes. This will have implications in the area of molecular coolants where CuII and GdIII are the preferred choice as they inherit no/negligible anisotropy, but our finding suggests that CuII invariably also offers strong exchange interaction – a parameter unsuitable for ideal molecular coolants. Metals ions such as MnII and CrIII are perhaps better choice for molecular refrigeration as they possess large spin values, negligible anisotropy and mediate relatively a weak magnetic exchange interaction.

On the role of black hole spin and accretion in powering relativistic jets in AGN

Motivated by the remarkable results on the general properties of blazars obtained from Fermi observations we discuss the role of spin and accretion in powering relativistic jets in AGNs. We consider studies of the Blandford–Znajek mechanism taking into account advection of magnetic flux from an accretion disk surrounding the Black Hole (BH) which indicate that the mechanism is inhibited for values of the BH spin a ≲ 0.5. However large scale propagation of the jet with highly relativistic bulk acceleration likely requires even larger spin values. The Blandford–Znajek mechanism then predicts a tight connection between jet power and accretion power, accounting for the correlation between γ–ray luminosity and accretion disk luminosity found in the bright Fermi blazar sample. The suggested spin threshold would lead to a grand unification of AGN based on only two intrinsic parameters: the BH spin and the accretion rate in Eddington units.

LIGHT-BENDING SCENARIO FOR ACCRETING BLACK HOLES IN X-RAY POLARIMETRY

We discuss a model of an X-ray illuminating source above an accretion disk of a rotating black hole. Within the so called lamp-post scheme we compute the expected (observed) polarization properties of the radiation reaching an observer. We explore the dependencies on model parameters, employing Monte Carlo radiation transfer computations of the X-ray reflection on the accretion disk and taking general relativity effects into account. In particular, we discuss the role of the black hole spin, of the observer viewing angle, and of the primary X-ray source distance from the black hole. We give several examples of the resulting polarization degree for two types of exemplary objects - active galactic nuclei and Galactic black holes. In order to assess potential observability of the polarization features, we assume the sensitivity of the proposed New Hard X-ray Mission (NHXM). We examine the energy range from several keV to ~50 keV, so the iron-line complex and the Compton hump are included in our model spectra. We find the resultant polarization degree to increase at the higher end of the studied energy band, i.e. at >~20 keV. Thus, the best results for polarimetry of reflection spectra should be achieved at the Compton hump energy region. We also obtain higher polarization degree for large spin values of the black hole, small heights of the primary source, and low inclination angles of the observer.