Spin Space Research Articles

Exploring Non-Abelian Geometric Phases in Spin-1 Ultracold Atoms.

The spin vector of a spin-1 system, unlike that of a spin-1/2 system, can lie anywhere on or inside the Bloch sphere representing the phase space. As a consequence, the geometrical and topological properties of the spin-1 phase space of quantum states are richer and require a generalization of Berry's phase. For special trajectories passing through the center of the Bloch sphere (singular loops), the geometric phase has a non-Abelian nature. Here, we experimentally explore this geometric phase for singular loops in a spin-1 quantum system using ultracold ^{87}Rb atoms confined in an optical trap using microwave and rf control fields.

Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance.

Phases of matter are usually identified through spontaneous symmetry breaking, especially regarding unconventional superconductivity and the interactions from which it originates. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated perovskite Sr2RuO4 is considered to be the only solid-state analogue to the superfluid 3He-A phase1,2, with an odd-parity order parameter that is unidirectional in spin space for all electron momenta and breaks time-reversal symmetry. This characterization was recently called into question by a search for an expected 'split' transition in a Sr2RuO4 crystal under in-plane uniaxial pressure, which failed to find any such evidence; instead, a dramatic rise and a peak in a single-transition temperature were observed3,4. Here we use nuclear magnetic resonance (NMR) spectroscopy of oxygen-17, which is directly sensitive to the order parameter via hyperfine coupling to the electronic spin degrees of freedom, to probe the nature of superconductivity in Sr2RuO4 and its evolution under strain. A reduction of the Knight shift is observed for all strain values and at temperatures below the critical temperature, consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results contradict a body of previous NMR work reporting no change in the Knight shift5 and the most prevalent theoretical interpretation of the order parameter as a chiral p-wave state. Sr2RuO4 is an extremely clean layered perovskite and its superconductivity emerges from a strongly correlated Fermi liquid, and our work imposes tight constraints on the order parameter symmetry of this archetypal system.

Scattering amplitudes as multi-particle higher-spin charges in the correspondence space

Following the proposal of Gelfond and Vasiliev (2016 J. High Energy Phys. JHEP10(2016)067), multi-particle scattering amplitudes are represented as conserved higher-spin (HS) charges. The advantage of such reformulation is that multi-particle amplitudes acquire the form of an integral of a closed form in the correspondence space unifying usual space-time with the twistor-like spinor space. This allows one to identify seemingly different formulae for amplitudes in terms of twistor and space-time integrals. An example of tree MHV amplitudes of Yang–Mills theory is considered in detail. Our results are derived using unfolded dynamics formulation of massless fields. In these terms all information on the amplitude is contained in a single function that, even for lower spin amplitudes, can be interpreted as a HS symmetry parameter. The proposed technique can be useful to relate different approaches to amplitude calculations.

Ferromagnetism and spin-valley liquid states in moiré correlated insulators

Motivated by the recent observation of evidences of ferromagnetism in correlated insulating states in systems with Moir\'{e} superlattices, we study a two-orbital quantum antiferromagnetic model on the triangular lattice, where the two orbitals physically correspond to the two valleys of the original graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$ symmetry, where the two SU(2) symmetries correspond to the rotation within the spin and valley space respectively. Through analytical argument, Schwinger boson analysis and also DMRG simulation, we find that even though all the couplings in the Hamiltonian are antiferromagnetic, there is still a region in the phase diagram with fully polarized ferromagnetic order. We argue that a Zeeman field can drive a metal-insulator transition in our picture, as was observed experimentally. We also construct spin liquids and topological ordered phases at various limits of this model. Then after doping this model with extra charge carriers, the system most likely becomes spin-triplet/valley-singlet $d+id$ topological superconductor as was predicted previously.

Dirac operators on the Fefferman spin spaces in almost CR-geometry

A spin structure on a contact Riemannian manifold carries a spin structure on a circle bundle over the manifold. We have interest in the Dirac operators associated with those structures. In terms of a modified Tanno connection, relations between them are studied and some kinds of their explicit expressions are offered.

Curvature-stabilized skyrmions with angular momentum

We examine skyrmionic field configurations on a spherical ferromagnet with large normal anisotropy. Exploiting variational concepts of angular momentum we find a new family of localized solutions to the Landau-Lifshitz equation that are topologically distinct from the ground state and not equivariant. Significantly, we observe an emergent spin-orbit coupling on the level of magnetization dynamics in a simple system without individual rotational invariance in spin and coordinate space.

Doppler shift in semi-Riemannian signature and the non-uniqueness of the Krein space of spinors

We give examples illustrating the fact that the different space/time splittings of the tangent bundle of a semi-Riemannian spin manifold give rise to nonequivalent norms on the space of compactly supported sections of the spinor bundle, and as a result, to different completions. We give a necessary and sufficient condition for two space/time splittings to define equivalent norms in terms of a generalized Doppler shift between maximal negative definite subspaces. We explore some consequences for the noncommutative geometry program.

Fractional spin-vortex states in F = 2 spinor Bose-Einstein condensates

Stable fractional vortices are numerically generated in the two-dimensional rotating F=2 spinor Bose-Einstein condensates. We demonstrate the existence of 14-vortex state or 12-vortex state in the biaxial nematic phase, and 13-vortex state in the cyclic phase. At fast rotation a lattice of fractional vortex in the spin space emerges. Intriguingly, the integral spin-winding of the whole system does not increase with the rotation speed but equals to a simple fraction.

New type of solutions of Yang-Baxter equations, quantum entanglement and related physical models

Starting from the Kauffman-Lomonaco braiding matrix transforming the natural basis to Bell states, the spectral parameter describing the entanglement is introduced through Yang-Baxterization. It gives rise to a new type of solutions for Yang-Baxter equation, called the type-II that differs from the familiar solution called type-I of YBE associated with the usual chain models. The Majorana fermionic version of type-II yields the Kitaev Hamiltonian. The introduced ℓ1-norm leads to the maximum of the entanglement by taking the extreme value and shows that it is related to the Wigner’s D-function. Based on the Yang-Baxter equation the 3-body S-Matrix for type-II is explicitly given. Different from the type-I solution, the type-II solution of YBE should be considered in describing quantum information. The idea is further extended to ℤ3 parafermion model based on SU(3) principal representation. The type-II is in difference from the familiar type-I in many respects. For example, the quantities corresponding to velocity in the chain models obey the Lorentzian additivity rather than Galilean rule (u + v). Most possibly, for the type-II solutions of YBE there may not exist RTT relation. Further more, for ℤ3 parafermion model we only need the rational Yang-Baxterization, which seems like trigonometric. Similar discussions are also made in terms of generalized Yang-Baxter equation with three spin spaces .

Longitudinal Spin Fluctuations and Magnetic Ordering Temperature in Metals: First-Principle Modeling and Phase Space Integration Measure

In magnetically ordered metals the magnitude of the local atomic moment become temperature dependent. To deal with this problem on the ab-initio level one need to employ a specific methodology for calculation of the electronic structure that takes into the account the magnetic disorder effects. In addition one needs to setup a special statistical models allowing simultaneously for ab-initio mapping and for the variation of the local spin magnitude. To this end here we discuss and employ methodology that is based on the Disordered Local Moment (DLM) formalism, spin-constraint Local Spin Density Approximation (LSDA) and Lichtenstein theorem for calculation of the inter-site exchange interactions. An extended classical Heisenberg Hamiltonian used for mapping allows for the variation of the lattice site spin magnitude. We consider here three representative canonical transition metals ferromagnets hcp Gd, bcc Fe and fcc Ni with quite a different character of the magnetic moment localization and illustrate the relative importance of the longitudinal spin fluctuations and the magnetic disorder induced electronic structure reconstruction. We use recently introduced linear measure [1] for integration over the longitudinal spin component in the classical configurational spin space.

Harmonic forms and spinors on the Taub-bolt space

This paper studies the space of L2 harmonic forms and L2 harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find all L2 zero modes of D̸A, the Dirac operator twisted by an arbitrary L2 harmonic connection A, and independently compute the index of D̸A. We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we generalise known results concerning harmonic spinors on Euclidean Schwarzschild.

Accelerating spin-space sampling by auxiliary spin dynamics and temperature-dependent spin-cluster expansion

Atomistic simulations of thermodynamic properties of magnetic materials rely on an accurate modelling of magnetic interactions and an efficient sampling of the high-dimensional spin space. Recent years have seen significant progress with a clear trend from model systems to material specific simulations that are usually based on electronic-structure methods. Here we develop a Hamiltonian Monte Carlo framework that makes use of auxiliary spin-dynamics and an auxiliary effective model, the temperature-dependent spin-cluster expansion, in order to efficiently sample the spin space. Our method does not require a specific form of the model and is suitable for simulations based on electronic-structure methods. We demonstrate fast warm-up and a reasonably small dynamical critical exponent of our sampler for the classical Heisenberg model. We further present an application of our method to the magnetic phase transition in bcc iron using magnetic bond-order potentials.

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.

Local broken symmetry and spin conductivity in the two-dimensional model in the compass lattice

The spin transport in the neighborhood of a quantum phase transition in the two-dimensional compass model is studied. The model presents Heisenberg compass interactions of amplitudes Jx and Jz and next and next-nearest neighbor Heisenberg interactions J1 and J2. Where the Heisenberg interactions are isotropic in spin space, but the compass interactions depending on the bond direction. Our results show a conductivity varying a little with the behavior of critical parameters η = J2∕J1, Jz and Jx. Hence, we obtain a little variation of the phase transition to magnetically ordered phase on conductivity. Besides, we obtain a conventional conductor behavior for the AC spin transport in the limit ω → 0 or DC limit.

Digging the population of compact binary mergers out of the noise

Coalescing compact binaries emitting gravitational wave (GW) signals, as recently detected by the Advanced LIGO-Virgo network, constitute a population over the multi-dimensional space of component masses and spins, redshift, and other parameters. Characterizing this population is a major goal of GW observations and may be approached via parametric models. We demonstrate hierarchical inference for such models with a method that accounts for uncertainties in each binary merger's individual parameters, for mass-dependent selection effects, and also for the presence of a second population of candidate events caused by detector noise. Thus, the method is robust to potential biases from a contaminated sample and allows us to extract information from events that have a relatively small probability of astrophysical origin.

Preferred Magnetic Excitations in the Iron-Based Sr_{1-x}Na_{x}Fe_{2}As_{2} Superconductor.

With spin-orbit coupling, both local-moment magnetism and itinerant electrons are expected to behave anisotropically in spin space, but such effects' influence on the formation of unconventional superconductivity has been hitherto unexplored. Here, in an iron-based superconductor, Sr_{1-x}Na_{x}Fe_{2}As_{2}, we report spectroscopic evidence that itinerant electrons "prefer" to be assisted by c-axis polarized magnetic excitations in their formation of superconducting Cooper pairs, against the polarization of the local-moment excitations. Our result naturally explains why the superconductivity competes strongly with the tetragonal magnetic phase in this material, and provides a fresh view on how to make a good superconductor out of a magnetic "Hund's metal."

Estimation of Neutrino Masses Without Using Seesaw Mechanism

We propose the Bethe-Salpeter-like amplitude of spin operator in spin space and consider that the vibration of this spin operator amplitude causes the vibration in azimuthal angle space, which causes the anomalous magnetic moment of leptons and generates masses of flavor state neutrino. Under this consideration, we can estimate neutrino masses using anomalous magnetic moment of leptons instead of using conventional seesaw mechanism. Electron anomalous magnetic moment and muon anomalous magnetic moment have been measured precisely so that we can estimate the masses of electron and muon neutrino systemically in our consideration. For tau neutrino mass case, we cannot estimate it in our consideration because tauon anomalous magnetic moment has not been measured. Instead, we use the squared mass splitting data to estimate tau neutrino mass in this paper. These are not mass eigenstates masses but flavor states masses, however, the sum of these masses, which should be equal to the sum of mass eigen states masses, is consistent to the current upper and lower bound of the sum of neutrino masses for both cases of normal hierarchy and inverted hierarchy.

Spin Splitting Induced in a Superconductor by an Antiferromagnetic Insulator.

Inspired by recent feats in exchange coupling antiferromagnets to an adjacent material, we demonstrate the possibility of employing them for inducing spin splitting in a superconductor, thereby avoiding the detrimental, parasitic effects of ferromagnets employed to this end. We derive the Gor'kov equation for the matrix Green's function in the superconducting layer, considering a microscopic model for its disordered interface with a two-sublattice magnetic insulator. We find that an antiferromagnetic insulator with effectively uncompensated interface induces a large, disorder-resistant spin splitting in the adjacent superconductor. In addition, we find contributions to the self-energy stemming from the interfacial disorder. Within our model, these mimic impurity and spin-flip scattering, while another breaks the symmetries in particle-hole and spin spaces. The latter contribution, however, drops out in the quasiclassical approximation and thus, does not significantly affect the superconducting state.

Modeling molecular magnets with large exchange and on-site anisotropies

Spins in molecular magnets can experience both anisotropic exchange interactions and on-site magnetic anisotropy. In this paper we study the effect of exchange anisotropy on the molecular magnetic anisotropy both with and without on-site anisotropy. When both the anisotropies are small, we find that the axial anisotropy parameter $D_M$ in the effective spin Hamiltonian is the sum of the individual contributions due to exchange and on-site anisotropies. We find that even for axial anisotropy of about $15\%$, the low energy spectrum does not correspond to a single parent spin manifold but has intruders states arising from other parent spin. In this case, the low energy spectrum can not be described by an effective Hamiltonian spanning the parent spin space. We study the magnetic susceptibility, specific heat as a function of temperature and magnetization as a function of applied field to characterize the system in this limit. We find that there is synergy between the two anisotropies, particularly for large systems with higher site spins.

Energy-momentum tensor of a ferromagnet

The energy-momentum tensor of a ferromagnet derived according to the standard prescription of Noether's theorem has a major flaw: the term originating from the spin Berry phase is gauge-dependent. As a consequence, some physical quantities computed from the tensor show unphysical behavior. For example, the presence of a spin-polarized current does not affect the energy of the domain wall in the commonly accepted gauge, which implies-incorrectly-the absence of the adiabatic spin torque. In other gauges, the spin torque shows unphysical glitches occurring when the plane of magnetization crosses the Dirac string associated with a magnetic monopole in spin space. We derive a gauge-invariant energy-momentum tensor that is free from these artifacts but requires the addition of an extra spatial dimension, with the ferromagnet living on its boundary. It can be obtained most directly from the Wess-Zumino action for spins, which relies on the same extra dimension.