Spin Rings Research Articles

Violation of ferromagnetic ordering of energy levels in spin rings for the singlet

Abstract We demonstrate a violation of the ‘ferromagnetic ordering of energy levels’ conjecture (FOEL) for even length spin rings. The FOEL conjecture was a guess made by Nachtergaele, Spitzer and an author for the Heisenberg model on certain graphs: a family of inequalities, the first of which is the statement that the spectral gap of the Heisenberg model equals the gap of the random walk. That first guess was originally a conjecture of Aldous which was later proved by Caputo, Liggett and Richthammer. We claim that for spin rings of even length L > 4, the lowest spin S = 0 energy is lower than the lowest spin S = 1 energy. This violates the ( L / 2 ) th inequality in the FOEL conjecture. Our methodology is largely numerical: we have applied exact diagonalization up to L = 20. We also rigorously consider the Hamiltonian of the Heisenberg spin ring for even length L projected to the spin S = 0 sector. We prove that it has a unique ground state. Then, using the single mode approximation the uniqueness explains the energy turn-around. Important insight comes from reconsideration of previous work by Sutherland, using the Bethe ansatz. Especially important is a work of Dhar and Shastry that goes beyond the Bethe ansatz.

Spin-Wave Model of Free Induction Decay in Ring Spin Cluster

Spin-Wave Model of Free Induction Decay in Ring Spin Cluster

A four-tensor momenta equation for rolling physics

Relativistic four-tensor equation dJ μ ν = M μ ν dt is developed to analyse linear translation with rotation processes. The postulated cause-effect four-tensor equation, a relativistic generalisation for classical angular-impulse–angular-momentum variation equation dJ = Mdt, includes the Poinsot-Euler rotation (angular-impulse–angular-momentum variation) equation, Newton’s second law (linear-impulse–linear-momentum variation equation), and thermodynamics first law (work–energy equation). This four-tensor formalism is applied to describe three linear translation with rotation processes: a ring rolling on the floor by a horizontal force linear impulse and torque, fulfilling the rolling condition (mechanical energy conservation), a spinning ring placed on the ground until achieved the rolling condition (mechanical energy dissipation by friction), and a fireworks wheel ascending an incline (mechanical energy production by decreasing a thermodynamic potential).

Separation of spherically and translationally covariant finite quantum spaces within the XXX model

Separation of spherically and translationally covariant finite quantum spaces within the XXX model

Spatial antiferromagnetic spin texture as a nano-oscillator

We report a theoretical study of the localized spatial magnetization configuration, which is a confined spin configuration of the target skyrmion/hopfion type in an antiferromagnet with perpendicular magnetic anisotropy, and then we solve the particular problem of self-oscillations of such a topological spin texture. Using the energy approach, a self-consistent account of inhomogeneity of the characteristics of the topological magnetic spin texture was carried out. On this basis, the equation of free oscillations of the confined spin configuration magnetization was derived and its quasi-classical solution was found. For a thin ring spin texture, the frequency, period of oscillations and relative amplitude of the main tone of oscillations are found. For the first time, we determined the topological mass, inertial mass and total energy of the main tone of oscillations of such spatial spin texture. The self-oscillatory process of a spatial spin texture is interpreted as a magnetic nano-oscillator.

Thermodynamics of the Spin Square

Small spin systems at the interface between analytical studies and experimental application have been intensively studied in recent decades. The spin ring consisting of four spins with uniform antiferromagnetic Heisenberg interaction is an example of a completely integrable system, in the double sense: quantum mechanical and classical. However, this does not automatically imply that the thermodynamic quantities of the classical system can also be calculated explicitly. In this work, we derive analytical expressions for the density of states, the partition function, specific heat, entropy, and susceptibility. These theoretical results are confirmed by numerical tests. This allows us to compare the quantum mechanical quantities for increasing spin quantum numbers s with their classical counterparts in the classical limit srightarrow infty . As expected, a good agreement is obtained, except for the low temperature region. However, this region shrinks with increasing s, so that the classical state variables emerge as envelopes of the quantum mechanical ones.

Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach

Recent work on approximating ground states of Heisenberg spin clusters by projected Hartree–Fock theory (PHF) is extended to a cluster-based ansatz (cPHF). Whereas PHF variationally optimizes a site–spin product state for the restoration of spin- and point-group symmetry, cPHF groups sites into discrete clusters and uses a cluster-product state as the broken-symmetry reference. Intracluster correlation is thus already included at the mean-field level, and intercluster correlation is introduced through symmetry projection. Variants of cPHF differing in the broken and restored symmetries are evaluated for ground states and singlet-triplet gaps of antiferromagnetic spin rings for various cluster sizes, where cPHF in general affords a significant improvement over ordinary PHF, although the division into clusters lowers the cyclical symmetry. In contrast, certain two- or three-dimensional spin arrangements permit cluster groupings compatible with the full spatial symmetry. We accordingly demonstrate that cPHF yields approximate ground states with correct spin- and point-group quantum numbers for honeycomb lattice fragments and symmetric polyhedra.

An experimental investigation on rewetting of a 54 pins fuel bundle under steam environment by radial jet injection

An experimental investigation on rewetting of a 54 pins fuel bundle under steam environment by radial jet injection

Performance Evaluation of Austempered Ductile Iron Camshaft Low Alloyed with Vanadium on an Electric Spin Rig Test

Arbomex S.A. de C. V. is one of the largest worldwide manufacturers of ductile cast iron camshafts, produced by means of the phenolic urethane no-bake sand mold casting method and cold box by stack molding technology. As a result of the development of high-strength ADIs, low alloyed with vanadium, for camshaft manufacturing, previous results were published on the as-cast process and the austempering heat treatments applied to the camshafts. In the present work, camshafts of ADIs, low alloyed with 0.2 and 0.3 wt.% V, were produced at austempering temperatures of 265 and 305 °C. The performance of the new camshafts was evaluated by wear testing to ensure the function and durability of the camshafts by means of the block-on-ring wear test and a valve train system to evaluate the volume loss of material removed and the geometrical changes of the camshaft, respectively. The ADIs heat treated to 265 °C showed a microstructure constituted of fine ausferrite that aided in obtaining the highest wear resistance in the block-on ring wear test. No wear or pitting evidence was detected on the camshaft lobes and roller surfaces after the OEM test protocol during the electric spin ring test at low and high conditions for the ADI alloyed with 0.2 wt.% V heat treated at 265 °C.

Robustness of energy landscape controllers for spin rings under coherent excitation transport

Abstract The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control and generates results in contradiction to the expectations of classical control theory. This paper examines the robustness of controllers designed to optimize the fidelity of an excitation transfer to uncertainty in system and control parameters. We use the logarithmic sensitivity of the fidelity error as the robustness measure, drawing on the classical control analog of the sensitivity of the tracking error. Our analysis shows that quantum systems optimized for coherent transport demonstrate significantly different correlation between error and the log-sensitivity depending on whether the controller is optimized for readout at an exact time T or over a time-window T ± Δ/2.

Analyzing and Unifying Robustness Measures for Excitation Transfer Control in Spin Networks

Recent achievements in quantum control have resulted in advanced techniques for designing controllers for applications in quantum communication, computing, and sensing. However, the susceptibility of such systems to noise and uncertainties necessitates robust controllers that perform effectively under these conditions to realize the full potential of quantum devices. The time-domain log-sensitivity and a recently introduced robustness infidelity measure (RIM) are two means to quantify controller robustness in quantum systems. The former can be found analytically, while the latter requires Monte-Carlo sampling. In this work, the correlation between the log-sensitivity and the RIM for evaluating the robustness of single excitation transfer fidelity in spin chains and rings in the presence of dephasing is investigated. We show that the expected differential sensitivity of the error agrees with the differential sensitivity of the RIM, where the expectation is over the error probability distribution. Statistical analysis also demonstrates that the log-sensitivity and the RIM are linked via the differential sensitivity, and that the differential sensitivity and RIM are highly concordant. This unification of two means (one analytic and one via sampling) to assess controller robustness in a variety of realistic scenarios provides a first step in unifying various tools to model and assess robustness of quantum controllers.

Cooling a long-range interacting system faster via applying an external magnetic field

If a mean-field spin ring interact with a cold external thermal reservoir, the system might first evolve to the paramagnetic metastable state along the paramagnetic path, and then fluctuate around the metastable state for a long period due to an energy barrier. The spin system must absorb sufficient energy from the thermal reservoir to achieve a phase transition to the final ferromagnetic equilibrium state. However, if an external magnetic field is applied to the system, the energy barrier becomes smaller, which can reduce the relaxation time of the system significantly. Moreover, if the magnetic intensity is strong enough, the energy barrier vanishes and the system evolves directly to the equilibrium state.

Odd thermodynamic limit for the Loschmidt echo

Is it possible to readily distinguish a system made by an Avogadro's number of identical elements and one with a single additional one? Usually, the answer to this question is negative but, in this work, we show that in antiferromagnetic quantum spin rings a simple out-of-equilibrium experiment can do so, yielding two qualitatively and quantitatively different outcomes depending on whether the system includes an even or an odd number of elements. We consider a local quantum-quench setup and calculate a generating function of the work done, namely, the Loschmidt echo, showing that it displays different features depending on the presence or absence of topological frustration, which is triggered by the even/oddness in the number of the chain sites. We employ the prototypical quantum Ising chain to illustrate this phenomenology, which we argue being generic for antiferromagnetic spin chains, as it stems primarily from the different low energy spectra of frustrated and non frustrated chains. Our results thus prove that these well-known spectral differences lead indeed to distinct observable characteristics and open the way to harvest them in quantum thermodynamics protocols.

Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model.

We study the ground-state properties of a quantum sunburst model, composed of a quantum Ising spin ring in a transverse field, symmetrically coupled to a set of ancillary isolated qubits, to maintain a residual translation invariance and also a Z_{2} symmetry. The large-size limit is taken in two different ways: either by keeping the distance between any two neighboring ancillary qubits fixed or by fixing their number while increasing the ring size. Substantially different regimes emerge, depending on the various Hamiltonian parameters: For small energy scale δ of the ancillary subsystem and small ring-qubit interaction κ, we observe rapid and nonanalytic changes in proximity to the quantum transitions of the Ising ring, both first order and continuous, which can be carefully controlled by exploiting renormalization-group and finite-size scaling frameworks. Smoother behaviors are instead observed when keeping δ>0 fixed and in the Ising disordered phase. The effect of an increasing number n of ancillary spins turns out to scale proportionally to sqrt[n] for sufficiently large values of n.

Designing Z2 and Z2×Z2 topological orders in networks of Majorana bound states

Topological orders have been intrinsically identified in a class of systems such as fractional quantum Hall states and spin liquids. Accessing such states often requires extreme conditions such as low temperatures, high magnetic fields, pure samples, etc. Another approach would be to engineer the topological orders in systems with more accessible ingredients. In this work, we present networks of Majorana bound states, which are currently accessible in semiconductor nanowires proximitized to conventional superconductors, and show that the effective low-energy theory is topologically ordered. We first demonstrate the main principles in a lattice made of Kitaev superconducting chains comprising both spin species. The lattice is coupled to free magnetic moments through the Kondo interaction. We then show that at the weak coupling limit, effective ring spin interactions are induced between magnetic moments with a topological order enjoying a local $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge symmetry. We then show that the same topological order and also the $\mathbb{Z}_2$ one can be engineered in architecture patterns of semiconductor nanowires hosting Majorana bound states. The basic blocks of patterns are the time-reversal Majorana Cooper boxes coupled to each other by metallic leads, and the Majorana states are allowed to tunnel to quantum dots sitting on the vertices of the lattices. In the limit of strong onsite Coulomb interactions, where the charge fluctuations are suppressed, the magnetic moments of dots on the square and honeycomb lattices are described by topologically ordered spin models with underlying $\mathbb{Z}_2$ and $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge symmetries, respectively. Finally, we show that the latter topological order can also be realized in a network of purely Majorana zero modes in the absence of coupling to quantum dots.

Ground states of Heisenberg spin clusters from projected Hartree-Fock theory

We apply the projected Hartree-Fock theory (PHF) for approximating ground states of Heisenberg spin clusters. Spin-rotational, point-group, and complex-conjugation symmetry are variationally restored from a broken-symmetry mean-field reference, where the latter corresponds to a product of local spin states. A fermionic formulation of the Heisenberg model furnishes a conceptual connection to PHF applications in quantum chemistry and detailed equations for a self-consistent field optimization of the reference state are provided. Different PHF variants are benchmarked for ground-state energies and spin-pair correlation functions of antiferromagnetic spin rings and three different polyhedra, with various values of the local spin-quantum number $s$. Although PHF is not suitable to study the thermodynamic limit (where it reduces to the conventional HF results), the low computational cost and the compact wave-function representation make PHF a promising complement to existing approaches for ground states of finite spin clusters, particularly for large local spin $s$ and a moderately large number of sites $N$. The present work may also motivate future explorations of more accurate post-PHF methods for Heisenberg spin clusters.

On‐Surface Synthesis and Collective Spin Excitations of a Triangulene‐Based Nanostar

AbstractTriangulene nanographenes are open‐shell molecules with predicted high spin state due to the frustration of their conjugated network. Their long‐sought synthesis became recently possible over a metal surface. Here, we present a macrocycle formed by six [3]triangulenes, which was obtained by combining the solution synthesis of a dimethylphenyl‐anthracene cyclic hexamer and the on‐surface cyclodehydrogenation of this precursor over a gold substrate. The resulting triangulene nanostar exhibits a collective spin state generated by the interaction of its 12 unpaired π‐electrons along the conjugated lattice, corresponding to the antiferromagnetic ordering of six S=1 sites (one per triangulene unit). Inelastic electron tunneling spectroscopy resolved three spin excitations connecting the singlet ground state with triplet states. The nanostar behaves close to predictions from the Heisenberg model of an S=1 spin ring, representing a unique system to test collective spin modes in cyclic systems.

On-Surface Synthesis and Collective Spin Excitations of a Triangulene-Based Nanostar.

Triangulene nanographenes are open‐shell molecules with predicted high spin state due to the frustration of their conjugated network. Their long‐sought synthesis became recently possible over a metal surface. Here, we present a macrocycle formed by six [3]triangulenes, which was obtained by combining the solution synthesis of a dimethylphenyl‐anthracene cyclic hexamer and the on‐surface cyclodehydrogenation of this precursor over a gold substrate. The resulting triangulene nanostar exhibits a collective spin state generated by the interaction of its 12 unpaired π‐electrons along the conjugated lattice, corresponding to the antiferromagnetic ordering of six S=1 sites (one per triangulene unit). Inelastic electron tunneling spectroscopy resolved three spin excitations connecting the singlet ground state with triplet states. The nanostar behaves close to predictions from the Heisenberg model of an S=1 spin ring, representing a unique system to test collective spin modes in cyclic systems.

Simulating Static and Dynamic Properties of Magnetic Molecules with Prototype Quantum Computers

Magnetic molecules are prototypical systems to investigate peculiar quantum mechanical phenomena. As such, simulating their static and dynamical behavior is intrinsically difficult for a classical computer, due to the exponential increase of required resources with the system size. Quantum computers solve this issue by providing an inherently quantum platform, suited to describe these magnetic systems. Here, we show that both the ground state properties and the spin dynamics of magnetic molecules can be simulated on prototype quantum computers, based on superconducting qubits. In particular, we study small-size anti-ferromagnetic spin chains and rings, which are ideal test-beds for these pioneering devices. We use the variational quantum eigensolver algorithm to determine the ground state wave-function with targeted ansatzes fulfilling the spin symmetries of the investigated models. The coherent spin dynamics are simulated by computing dynamical correlation functions, an essential ingredient to extract many experimentally accessible properties, such as the inelastic neutron cross-section.

Bosonic resonating valence bond theory of the possible chiral spin-liquid state in the triangular-lattice Hubbard model

Recent numerical simulations find a possible chiral spin-liquid state in the intermediate coupling regime of the triangular lattice Hubbard model. Here we provide a simple picture for its origin in terms of a bosonic resonating valence bond (RVB) description. More specifically, we show that such a chiral spin-liquid state can be understood as a quantum disordered tetrahedral spin state stabilized by the four spin ring exchange coupling, which suppresses the order-by-disorder effect toward a stripy spin state. Such a chiral spin-liquid state features a spin Berry phase of $\frac{\ensuremath{\pi}}{2}$ per triangle. However, we show that the topological property of such a state is totally missed in the Schwinger boson mean-field description as a result of the lack of boson rigidity caused by the no double occupancy constraint.