Spin Space Research Articles

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.

Three-dimensional interferometric imaging and micromotion feature extraction of spinning space debris in low-resolution radar

Inspired by the idea of multiantenna interferometric processing in interferometric inverse synthetic aperture radar, based on monostatic low-resolution narrowband radar with three antennas, a three-dimensional (3-D) interferometric imaging and micromotion feature extraction method for spinning space debris is proposed. First, the micromotion characteristic of the target in low-resolution radar is explained. Next, by taking advantage of the target’s micro-Doppler characteristic on time-frequency (TF) domain, the time-varying two-dimensional imaging of scatterers in both the normal mode and the squint mode is achieved through interferometric processing. Finally, the height information of scatterers is solved by an ellipse fitting-based method; thus 3-D imaging for the spinning space debris is realized. Meanwhile, some 3-D micromotion features are exactly extracted during imaging, and the relevant issues, including window width determination of TF analysis, scatterer separation, and noise suppression are discussed in detail. Simulation results in diverse occasions validate the effectiveness and the robustness of the method.

Multielectron geometric phase in intensity interferometry

Pancharatnam phase was discovered in the context of polarization optics in nineteen fifties. However, its full realization in quantum many-body systems still eludes us. This is primarily due to the fact that electron spin is not easily tunable. In the present proposal, we suggest that edge states of quantum spin Hall effect (QSHE) in conjunction with spin polarized electrodes (SPE) provide us with a unique opportunity to explore the Pancharatnam phase. We demonstrate the possibility of generating and detecting the multi-electron version of this phase that can as well be interpreted as multi-particle Aharonov-Bohm (A-B) effect in spin space arising solely due to spin dynamics. We further show that our proposed set-up leads to a robust interference pattern which survives orbital dephasing.

Generalized Josephson relation for conserved charges in multicomponent bosons

The Josephson relation is generalized for conserved charges in multi-component bosons. With linear response theory, a formula for derivation of generalized superfluid density is given. When there are several conserved charges, the superfluid density is generally a second order tensor in internal spin space. When the rank of Green's function matrix is one, Josephson relation is given explicitly with phase operator method. For two-component bosons, with quantum field theory, we show a generalized Hugenholtz-Pines relation hold and existence of two gapless phonons. When the interactions are $U(2)$ invariant, we show there is a gapless quadratic dispersion excitation no matter how strong the interactions are. The corresponding generalized Josephson relation is expressed with Green's function matrix elements.

Symmetry-restoring quantum phase transition in a two-dimensional spinor condensate

Bose Einstein condensates of spin-1 atoms are known to exist in two different phases, both having spontaneously broken spin-rotation symmetry, a ferromagnetic and a polar condensate. Here we show that in two spatial dimensions it is possible to achieve a quantum phase transition from a polar condensate into a singlet phase symmetric under rotations in spin space. This can be done by using particle density as a tuning parameter. Starting from the polar phase at high density the system can be tuned into a strong-coupling intermediate-density point where the phase transition into a symmetric phase takes place. By further reducing the particle density the symmetric phase can be continuously deformed into a Bose-Einstein condensate of singlet atomic pairs. We calculate the region of the parameter space where such a molecular phase is stable against collapse.

Phase transitions for a model with uncountable spin space on the Cayley tree: the general case

In this paper we complete the analysis of a statistical mechanics model on Cayley trees of any degree, started in Botirov (Positivity 21(3):955–961, 2017), Eshkabilov et al. (J Stat Phys 147(4):779–794, 2012), Eshkabilov and Rozikov (Math Phys Anal Geom 13:275–286, 2010), Botirov et al. (Lobachevskii J Math 34(3):256–263 2013) and Jahnel et al. (Math Phys Anal Geom 17:323–331 2014). The potential is of nearest-neighbor type and the local state space is compact but uncountable. Based on the system parameters we prove existence of a critical value $$\theta _{\mathrm{c}}$$ such that for $$\theta \le \theta _{\mathrm{c}}$$ there is a unique translation-invariant splitting Gibbs measure. For $$\theta _{\mathrm{c}}<\theta $$ there is a phase transition with exactly three translation-invariant splitting Gibbs measures. The proof rests on an analysis of fixed points of an associated non-linear Hammerstein integral operator for the boundary laws.

Temperature dependence of nonlinear susceptibilities in an infinite range interaction model

We present a model to probe metamagnetic properties in systems with a variable number of interacting spins. Thermodynamic properties such as the magnetization per particle , linear susceptibility , and nonlinear susceptibilities and were calculated. The model produces a different magnetic response for N particles when comparing to N − 1 particles for small . For an even number of particles, the susceptibilities show maxima in their temperature dependence. An odd number produces an additional free spin response that dominates at low temperatures. This free spin response also produces a step in the field-dependent magnetization per particle at B = 0 for odd N. The magnetization shows N/2 steps at with integer n for even N and additional steps at with integer n for odd N. Small clusters respond with metamagnetism in an otherwise isotropic spin space, while the large clusters show no metamagnetism.

A topological phase transition in topological insulator thin films exposed to an off-resonant light and its associated topological configuration

Surface-related properties of the three-dimensional topological insulators with/without considerable thickness are thought as the furthermost demandable in the field of condensed matter physics because of its rich technological applications. Motivated by these properties, we consider low energy effective Hamiltonian of three-dimensional topological insulators having a negligible thickness in the presence of irradiated off-resonant circularly polarized light to assess it's topological features. By evaluating the surface pseudo-spin Chern number analytically, we find that three dimensional topological insulator thin films pass through a phase transition from quantum pseudo spin Hall (QPSH) state to a photo-induced quantum Hall (P-QH) state when the effective energy induced by the circularly polarized light becomes greater in magnitude than the effective energy induced by the coupling between the top and bottom surfaces. We find that both the QPSH and P-QH states present a pronounced step-wise character. The phase-transition between these two topological states can be controlled by the degree of hybridization and off-resonant circularly polarized light. Additionally, we analyze the topological structure of QPSH and P-QH states by mapping the three-dimensional unit vector on a unit sphere and reveal that they display merons-like or anti-merons-like configurations in the real spin space.

Disorder-free spin glass transitions and jamming in exactly solvable mean-field models

We construct and analyze a family of MM-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity c=\alpha Mc=αM and becomes exactly solvable in the limit of large number of components M \to \inftyM→∞. We consider generic pp-body interactions between the vectorial Ising/continuous spins with linear/non-linear potentials. The existence of self-generated randomness is demonstrated by showing that the random energy model is recovered from a MM-component ferromagnetic pp-spin Ising model in M \to \inftyM→∞ and p \to \inftyp→∞ limit. In our systems the quenched disorder, if present, and the self-generated disorder act additively. Our theory provides a unified mean-field theoretical framework for glass transitions of rotational degree of freedoms such as orientation of molecules in glass forming liquids, color angles in continuous coloring of graphs and vector spins of geometrically frustrated magnets. The rotational glass transitions accompany various types of replica symmetry breaking. In the case of repulsive hardcore interactions in the spin space, the criticality of the jamming or SAT/UNSTAT transition becomes the same as that of hardspheres.

Holonomy rigidity for Ricci-flat metrics

On a closed connected oriented manifold M we study the space $$\mathcal {M}_\Vert (M)$$ of all Riemannian metrics which admit a non-zero parallel spinor on the universal covering. Such metrics are Ricci-flat, and all known Ricci-flat metrics are of this form. We show the following: The space $$\mathcal {M}_\Vert (M)$$ is a smooth submanifold of the space of all metrics and its premoduli space is a smooth finite-dimensional manifold. The holonomy group is locally constant on $$\mathcal {M}_\Vert (M)$$ . If M is spin, then the dimension of the space of parallel spinors is a locally constant function on $$\mathcal {M}_\Vert (M)$$ .

Synthesis of Majorana mass terms in low-energy quantum systems

We discuss the problem of how Majorana mass terms can be generated in low-energy systems. We show that, while these terms imply the Majorana condition, the opposite is not always true when more than one flavour is involved. This is an important aspect for the low-energy realizations of the Majorana mass terms exploiting superfluid pairings, because in this case the Majorana condition is not implemented in the spinor space, but in an internal (flavour) space. Moreover, these mass terms generally involve opposite effective chiralities, similarly to a Dirac mass term. The net effect of these features is that the Majorana condition does not imply a Majorana mass term. Accordingly the obtained Majorana spinors, as well as the resulting symmetry breaking pattern and low-energy spectrum, are qualitatively different from the ones known in particle physics. This result has important phenomenological consequences, e.g. implies that these mass terms are unsuitable to induce an effective see-saw mechanism, proposed to give mass to neutrinos. Finally, we introduce and discuss schemes based on space-dependent pairings with nonzero total momentum to illustrate how genuine Majorana mass terms may emerge in low-energy quantum systems.

A new algebraic structure in the standard model of particle physics

We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea, in brief, is to represent A (the algebra of differential forms on some possibly-noncommutative space) on H (the Hilbert space of spinors on that space); and to reinterpret this representation as a simple super-algebra B = A ⊕ H with even part A and odd part H. B is the fundamental object in our approach: we show that (nearly) all of the basic axioms and assumptions of the traditional real-spectral-triple formalism of NCG are elegantly recovered from the simple requirement that B should be a differential graded ∗-algebra (or “∗-DGA”). Moreover, this requirement also yields other, new, geometrical constraints. When we apply our formalism to the NCG traditionally used to describe the standard model of particle physics, we find that these new constraints are physically meaningful and phenomenologically correct. In particular, these new constraints provide a novel interpretation of electroweak symmetry breaking that is geometric rather than dynamical. This formalism is more restrictive than effective field theory, and so explains more about the observed structure of the standard model, and offers more guidance about physics beyond the standard model.

Skein relations for spin networks, modifed

An alternative framework underlying connection between tensor [Formula: see text]-calculus and spin networks is suggested. New sign convention for the inner product in the dual spinor space leads to a simpler and direct set of initial rules for the diagrammatic recoupling methods. Yet, it preserves the standard chromatic graph evaluations. In contrast with the standard formulation, the background space is that of symmetric tensor spaces, which seems to be in accordance with the representation theory of [Formula: see text]. An example of Apollonian disk packing is shown to be a source of spin networks. The graph labeling is extended to non-integer values, resulting in the complex values of chromatic evaluations.

Virtual walks in spin space: A study in a family of two-parameter models.

We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalized two-parameter family of spin models characterized by parameters y and z [de Oliveira etal., J. Phys. A 26, 2317 (1993)JPHAC50305-447010.1088/0305-4470/26/10/006]. The behavior of S(x,t), the probability that the walker is at position x at time t, is studied in detail. In general S(x,t)∼t^{-α}f(x/t^{α}) with α≃1 or 0.5 at large times depending on the parameters. In particular, S(x,t) for the point y=1,z=0.5 corresponding to the Voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size L as L^{2}logL. We also show that as the Voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution S(x,t) diverges in a power law manner with different exponents. For the majority Voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other nonequilibrium methods.

Teorias de gauge a la Utiyama

Resumo Revisamos a construção da teoria de gauge para os grupos de Lie semi-simples realizada por Utiyama em seu trabalho “Interpretação da Interação por Invariância Teórica”[1]. Mostramos que para manter a invariância de um sistema de campos ϕ A ( x ) sob um grupo de transformações a n parâmetros ϵ a ( x ) dependentes do ponto x μ é necessário introduzir um novo campo A μ a ( x ). Este campo auxiliar interage com ϕ como manifesto pela derivada covariante ∇ μ ϕ A. Determinamos a lei de transformação de A μ a sob o grupo mencionado e calculamos o tensor intensidade de campo F μ ν a x. Especificamos, ainda, a corrente conservada J a μ associada à invariância do sistema completo. Encerramos aplicando a teoria aos casos da partícula carregada em um campo eletromagnético e do potencial de Yang-Mills sob transformações de um campo de spin isotópico; fazemos breves comentários sobre o campo gravitacional como teoria de gauge e sobre a extensão da teoria de Utiyama na situação em que L A = L A A μ a ; ∂ ν A μ a ; ∂ ρ ∂ ν A μ a x.

Longitudinal integration measure in classical spin space and its application to first-principle based simulations of ferromagnetic metals

The classical Heisenberg type spin Hamiltonian is widely used for simulations of finite temperature properties of magnetic metals often using parameters derived from first principles calculations. In itinerant electron systems, however, the atomic magnetic moments vary their magnitude with temperature and the spin Hamiltonian should thus be extended to incorporate the effects of longitudinal spin fluctuations (LSF). Although the simple phenomenological spin Hamiltonians describing LSF can be efficiently parameterized in the framework of the constrained Local Spin Density Approximation (LSDA) and its extensions, the fundamental problem concerning the integration in classical spin space remains. It is generally unknown how to integrate over the spin magnitude. Two intuitive choices of integration measure have been used up to date – the Murata-Doniach scalar measure and the simple three dimensional vector measure. Here we derive the integration measure by considering a classical limit of the quantum Heisenberg spin Hamiltonian under conditions leading to the proper classical limit of the commutation relations for all values of the classical spin magnitude and calculate the corresponding ratio of the number of quantum states. We show that the number of quantum states corresponding to the considered classical spin magnitude is proportional to this magnitude and thus a non-trivial integration measure must be used. We apply our results to the first-principles simulation of the Curie temperatures of the two canonical ferromagnets bcc Fe and fcc Ni using a single-site LSF Hamiltonian with parameters calculated in the LSDA framework in the Disordered Local Moment approximation and a fixed spin moment constraint. In the same framework we compare our results with those obtained from the scalar and vector measures.

Homogeneous spin Riemannian manifolds with the simplest Dirac operator

Abstract We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds (M, g) which are traceless cyclic with respect to some quotient expression M = G/K and reductive decomposition 𝔤 = 𝔨 ⊕ 𝔪. Using transversally symmetric fibrations of noncompact type, we give a list of them.

Group theoretical approach to the Dirac operator on S2

In this revision we outline the group theoretical approach to formulate and solve the eigenvalue problem of the Dirac operator on the round 2-sphere conceived as the right coset S2 = SU(2)/U(1). Starting from general symmetry considerations we illustrate the formulation of the Dirac operator through left action or right action differential operators, whose properties on a right coset are quite different. The construction of the spinor space and the solution of the spectral problem using group theoretical methods is also presented.

Neutron Spin Resonance in the 112-Type Iron-Based Superconductor.

We use inelastic neutron scattering to study the low-energy spin excitations of the 112-type iron pnictide Ca_{0.82}La_{0.18}Fe_{0.96}Ni_{0.04}As_{2} with bulk superconductivity below T_{c}=22 K. A two-dimensional spin resonance mode is found around E=11 meV, where the resonance energy is almost temperature independent and linearly scales with T_{c} along with other iron-based superconductors. Polarized neutron analysis reveals the resonance is nearly isotropic in spin space without any L modulations. Because of the unique monoclinic structure with additional zigzag arsenic chains, the As 4p orbitals contribute to a three-dimensional hole pocket around the Γ point and an extra electron pocket at the X point. Our results suggest that the energy and momentum distribution of the spin resonance does not directly respond to the k_{z} dependence of the fermiology, and the spin resonance intrinsically is a spin-1 mode from singlet-triplet excitations of the Cooper pairs in the case of weak spin-orbital coupling.