Spin Block Research Articles

On mixing of Markov chains: coupling, spectral independence, and entropy factorization

For general spin systems, we prove that a contractive coupling for an arbitrary local Markov chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a large class of Markov chains including the Glauber dynamics, arbitrary heat-bath block dynamics, and the Swendsen-Wang dynamics. This reveals a novel connection between probabilistic techniques for bounding the convergence to stationarity and analytic tools for analyzing the decay of relative entropy. As a corollary of our general results, we obtain O(nlogn) mixing time and Ω(1∕n) modified log-Sobolev constant of the Glauber dynamics for sampling random q-colorings of an n-vertex graph with constant maximum degree Δ when q>(11∕6−ϵ0)Δ for some fixed ϵ0>0. We also obtain O(logn) mixing time and Ω(1) modified log-Sobolev constant of the Swendsen-Wang dynamics for the ferromagnetic Ising model on an n-vertex graph of constant maximum degree when the parameters of the system lie in the tree uniqueness region. At the heart of our results are new techniques for establishing spectral independence of the spin system and block factorization of the relative entropy. On one hand we prove that a contractive coupling of any local Markov chain implies spectral independence of the Gibbs distribution. On the other hand we show that spectral independence implies factorization of entropy for arbitrary blocks, establishing optimal bounds on the modified log-Sobolev constant of the corresponding block dynamics.

Full counting statistics in the gapped XXZ spin chain

We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse magnetisation in a large spin block of length ℓ. We found that for a subsystem of even length the full counting statistics is Gaussian, while for odd subsystems it is the sum of two Gaussian distributions. We test our analytic predictions with accurate tensor networks simulations. As a byproduct, we also obtain the symmetry (magnetisation) resolved entanglement entropies.

Reaction pathways for surface activated rubber particles

This paper studies molecular level interaction mechanisms involved in surface activation of rubber particles when exposed to a newly developed bio-modifier and microwave irradiation. It further examines how surface activation of rubber promotes its interaction with asphalt molecules to reduce phase separation in rubberized asphalt-binder. Using quantum-based calculations, chain reactions between an amide-rich bio-modifier and irradiated molecules of rubber is examined. The density functional theory (DFT)-based molecular modeling was performed on amide-type molecules as representatives for the bio-modifier. Comparing interactions of amidyl radical (RCO-N•H) of bio-modifier with sulfur-centered and carbon-centered radicals of rubber showed that amidyl radicals have higher affinity to bind to carbon-centered radicals than to sulfur-centered radicals. While the spine triplet state for ‒N…S‒ reaction coordinates encounters the obstacle of spin block and activation barrier, no spin block is observed on the ‒N…C‒ reaction pathway. The latter reaction was further observed via FTIR spectra where a new peak appeared at 1040 cm−1 indicating formation of CN bonds. Aforementioned reactions led to grafting highly polar molecules of bio-modifier onto the surface of rubber increasing rubber’s surface polarity. This was evidenced by the increase in acid-base component of rubber’s surface energy from 2.9 mJ/m2 in control rubber to 14.6 mJ/m2 in treated rubber. The increased polarity increased the interactions of rubber with asphalt molecules reducing the phase separation commonly known as segregation in rubberized asphalt. The latter was reflected in reduction of differences in complex modulus (G*) between top and bottom parts of rubberized asphalt specimens from 53.69% to 0.05%.

Synthesis, crystal structure and spin exchange coupling in polynuclear carboxylates with {Li2(VO)2} metal core

Crystals of binuclear complex [(VO)2(µ-OH)(µ-Piv)2(bpy)2](OTf) (1) have been obtained by the reaction of [VO(H2O)5](OTf)2 (OTf=CF3SO3−, Piv=(CH3)3CCO2−) with 2,2′-bipyridine (bpy) and lithium trimethylacetate (pivalate), Li(Piv), in a ratio of 1:1:2 in MeCN. Change of the reagent ratio to 1:1:3 resulted in the bimetallic compound [Li2(VO)2(µ-Piv)6(bpy)2] (2), which was isolated in the form of 2·MeCN and 2·CH2Cl2 solvates. Replacement of Li(Piv) with lithium trifluoroacetate Li(Tfac) (Tfac=CF3CO2−) results in the bimetallic compound [Li2(VO)2(µ-Tfac)6(bpy)2] (3). A similar reaction with lithium trichloroacetate, Li(Tcac) (Tcac=CCl3CO2−), in ethanol gives the mononuclear complex [VO(Tcac)(bpy)2](OTf) (4). The structures of 1–4 were determined by single crystal X-ray diffraction. The magnetic properties (2–300K) and EPR spectra of compounds 1–3 have been studied. Using the ESEEM (electron spin echo envelope modulation) method it has been shown that the mononuclear cation [VO(Tcac)(bpy)2]+ of complex 4 has partial spin density transfer from the VIV atom to donor ligands (in particular, the bpy nitrogen atoms). According to EPR spectroscopy data and quantum-chemical calculations, a similar spin density distribution is observed for 2 and 3, though spin exchange in these compounds is hindered by lithium ions, which contain no spin density and block electron density delocalization in the bridging system between the “magnetic” vanadium ions. Electrochemical properties of compounds 2 and 3 confirm the vanadium(IV) oxidation state.

Orbital-selective Mott phases of a one-dimensional three-orbital Hubbard model studied using computational techniques

A recently introduced one-dimensional three-orbital Hubbard model displays orbital-selective Mott phases with exotic spin arrangements such as spin block states [J. Rincón etal., Phys. Rev. Lett. 112, 106405 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.106405]. In this publication we show that the constrained-path quantum Monte Carlo (CPQMC) technique can accurately reproduce the phase diagram of this multiorbital one-dimensional model, paving the way to future CPQMC studies in systems with more challenging geometries, such as ladders and planes. The success of this approach relies on using the Hartree-Fock technique to prepare the trial states needed in CPQMC. We also study a simplified version of the model where the pair-hopping term is neglected and the Hund coupling is restricted to its Ising component. The corresponding phase diagrams are shown to be only mildly affected by the absence of these technically difficult-to-implement terms. This is confirmed by additional density matrix renormalization group and determinant quantum Monte Carlo calculations carried out for the same simplified model, with the latter displaying only mild fermion sign problems. We conclude that these methods are able to capture quantitatively the rich physics of the several orbital-selective Mott phases (OSMP) displayed by this model, thus enabling computational studies of the OSMP regime in higher dimensions, beyond static or dynamic mean-field approximations.

Quantum Correlation in Matrix Product States of One-Dimensional Spin Chains**Supported by the National Natural Science Foundation of China under Grant No. 10974137 and the Major Natural Science Foundation of the Educational Department of Sichuan Province under Grant No. 14ZA0167

For our proposed composite parity-conserved matrix product state (MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.

Magnetic fan structures in Ba0.5Sr1.5Zn2Fe12O22hexaferrite revealed by resonant soft x-ray diffraction

The hexaferrites are known to exhibit a wide range of magnetic structures, some of which are connected to important technological applications and display magnetoelectric properties. We present data on the low field magnetic structures stabilised in a Y-type hexaferrite as observed by resonant soft X-ray diffraction. The helical spin block arrangement that is present in zero applied magnetic field becomes fan-like as a field is applied in plane. The propagation vectors associated with each fan structure are studied as a function of field, and a new magnetic phase is reported. Mean field calculations indicate this phase should stabilise close to the boundary of the previously reported phases.

Topological invariant for generic one-dimensional time-reversal-symmetric superconductors in class DIII

A one dimensional time reversal symmetric topological superconductor (symmetry class DIII) features a single Kramers pair of Majorana bound states at each of its ends. These holographic quasiparticles are non-Abelian anyons that obey Ising-type braiding statistics. In the special case where an additional U(1) spin rotation symmetry is present, this state can be understood as two copies of a Majorana wire in symmetry class D, one copy for each spin block. We present a manifestly gauge invariant construction of the topological invariant for the generic case, i.e., in the absence of any additional symmetries like spin rotation symmetry. Furthermore, we show how the presence of inversion symmetry simplifies the calcuation of the topological invariant. The proposed scheme is suitable for the classification of both interacting and disordered systems and allows for a straightforward numerical evaluation of the invariant since it does not rely on fixing a continuous phase relation between Bloch functions. Finally, we apply our method to compute the topological phase diagram of a Rashba wire with competing s-wave and p-wave superconducting pairing terms.

Entanglement property in matrix product spin systems

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy Sn of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.

Temperature-dependent magnetic second-harmonic generation from Fe nanostructures grown on vicinal W(110)

Temperature-dependent magnetic second-harmonic generation (MSHG) at normal incidence (NI) is used to determine magnetization curves from Au-capped ultrathin Fe nanostructures grown on a vicinal W(110) substrate. Aligned magnetic nanostructures grown on low-symmetry interfaces are generally inhomogeneous, with different magnetic species, such as terrace and step atoms, contributing to the overall magnetic response from the interfacial regions. A phenomenological model of NI MSHG intensity and contrast at magnetic interfaces of 1 m symmetry is used to extract the magnetization information. Two characteristic temperatures are identified for both 0.75 and 2.0 monolayers of Fe, and it is proposed that the increased sensitivity of SHG to step atoms, compared to linear optical techniques, allows the contribution of boundary atoms to the spin block response to be directly detected at lower temperatures. The behavior of boundary spins such as these is expected to be important for atomic-scale magnetic structures.

Maximal Strings in the Crystal Graph of Spin Representations of the Symmetric and Alternating Groups

We define a block-reduced version of the crystal graph of spin representations of the symmetric and alternating groups, and separate it into layers, each obtained by translating the previous layer and, possibly, adding new defect zero blocks. We demonstrate that each layer has weight-preserving central symmetry, and study the sequence of weights occurring in the maximal strings. The Broué conjecture, that a block with abelian defect group is derived equivalent to its Brauer correspondent, has been proven for blocks of cyclic defect group and verified for many other blocks. This article is part of a study of the spin block case.

A comprehensive performance and energy consumption analysis of scheduling alternatives in clusters

In this paper, we conduct an in-depth evaluation of a broad spectrum of scheduling alternatives for clusters. These include the widely used batch scheduling, local scheduling, gang scheduling, most prior communication-driven coscheduling algorithms-Dynamic Coscheduling (DCS), Spin Block (SB), Periodic Boost (PB), and Co-ordinated Coscheduling (CC)-and a newly proposed HYBRID coscheduling algorithm on a 16-node, Myrinet-connected Linux cluster. Performance and energy measurements using several NAS, LLNL and ANL benchmarks on the Linux cluster provide several conclusions. First, although batch scheduling is currently used in most clusters, the blocking-based coscheduling techniques such as SB, CC and HYBRID and the gang scheduling can provide much better performance even in a dedicated cluster platform. Second, in contrast to some of the prior studies, we observe that blocking-based schemes like SB and HYBRID can provide better performance than spin-based techniques like PB on a Linux platform. Third, the proposed HYBRID scheduling provides the best performance-energy behavior and can be implemented on any cluster with little effort. All these results suggest that blocking-based coscheduling techniques are viable candidates to be used in clusters for significant performance-energy benefits.

Performance Comparison of Coscheduling Algorithms for Non-Dedicated Clusters Through a Generic Framework

In this paper, we address several key issues in designing coscheduling algorithms for clusters. First, we propose a generic framework for deploying coscheduling techniques by providing a reusable and dynamically loadable kernel module. Second, we implement several communication-driven coscheduling algorithms [ dynamic coscheduling (DCS), spin block (SB) and periodic boost (PB)] on a 16- node Linux cluster using the above framework. Third, with exhaustive experimentation using mixed workloads, we observe that unlike PB, which provided the best performance on a Solaris platform, the SB scheme outperforms all other techniques on a Linux platform. Finally, we investigate the impact of several job placement strategies, multiprogramming level (MPL), communication intensity and CPU and I/O intensive jobs on the performance of these coscheduling schemes. The experimental results show that the blocking-based coscheduling scheme (SB) has better tolerance to system workload variation compared with the spin-based schemes (DCS and PB), and overall, the blocking-based coscheduling scheme seems a better choice for non-dedicated Linux clusters.

Spin block inclusions

In this paper we classify all block equalities and all nontrivial block inclusions for spin blocks of the double covers of the symmetric groups at different odd primes. More generally, we describe for an odd integer s > 1 explicitly when an s ¯ -block of bar partitions is contained in a t ¯ -block of bar partitions, for t > 1 an odd integer or t = 4 . The question of block equality leads to the study of ( s ¯ , t ¯ ) -cores. In the case of primes they label spin characters which are of defect 0 for different primes and therefore represent a block equality. We enumerate these cores and show that there is a unique maximal one.

High-Spin Diimine Complexes of Iron(II) Reject Binding of Carbon Monoxide: Theoretical Analysis of Thermodynamic Factors Inhibiting or Favoring Spin-Crossover

A new series of Fe(II) complexes, FeCl2[N(R)=C(Me)C(Me)=N(R)], containing diimine ligands with hemilabile sidearms R (R = CH2(CH2)2NMe2, 1, CH2(CH2)2OMe, 2, CH2(CH2)2SMe), 3) were synthesized. The crystal structure of 1 showed 6-coordination where both amine arms were attached, whereas 2 was a 5-coordinate 16e species with one methoxy arm dangling free. Extensive attempts were made to bind CO to these species to synthesize precursors for dihydrogen complexes but were unsuccessful. Reaction of 1 with 1 or 2 equiv of AgOTf under CO atmosphere resulted in isolation of only a 6-coordinate bis(triflate)-containing product [Fe[N(R)=C(Me)C(Me)=N(R)](OTf)2] (R = CH2(CH2)2NMe2), 5. Reaction of 5-coordinate 2 with AgSbF6 under CO did not give a CO adduct but afforded instead a dicationic dinuclear complex [Fe[N(R)=C(Me)C(Me)=N(R)](mu-Cl)]2[SbF6]2 (R = CH2(CH2)2OMe), 4, containing a weakly bound SbF6. Thus coordination of hard-donor anions to iron was favored over CO binding. The unexpected rejection of binding of CO is rationalized by the iron being in a high-spin state in this system and energetically incapable of spin crossover to a low-spin state. Theoretical calculations on CO interaction with Fe(II) centers in spin states S = 0, 1, and 2 for both the 16e complexes and their CO adducts aid further understanding of this problem. They show that interaction of CO with a high-spin 5-coordinate Fe model diimine complex is essentially thermoneutral but is exergonic by about 48 kcal/mol to a comparable but low-spin diphosphine fragment. Spin crossover is thus disfavored thermodynamically rather than kinetically (e.g. a "spin block" effect); i.e., the ligand field strengths of the primarily N-donor groups are apparently insufficient to give a low-spin CO adduct.

Fine-grained entanglement loss along renormalization-group flows

We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along RG trajectories from the properties of the vacuum only, without need to study the whole hamiltonian.

Open shell organometallics: a general analysis of their electronic structure and reactivity

Transition metal organometallic compounds that contain fewer than 18-electrons and two or more unpaired electrons are generally excluded from treatises of either Werner-type coordination compounds or organometallic chemistry. However, they can be seen as the bridge filling the gap between these two traditional areas of coordination chemistry. Their magnetic and optical properties are reminiscent of the Werner-type complexes, whereas their chemical reactivity parallels that of the lower-valent organometallics. Spin state change phenomena are of paramount importance in this area. This paper provides a broad perspective of this area, with particular attention to: (i) how the ground state properties can be related to the metal and ligands nature; (ii) under which circumstances the often inappropriately invoked concept of “spin block” is meaningful; (iii) the spin acceleration concept; (iv) how the coordination sphere affects the topology of the reaction coordinate in the vicinity of spin crossing points; and (v) the effect of spin state changes on reaction selectivities.

Magnetoresistance of a domain wall at a submicron junction

A local magnetoresistance (MR) effect associated with the switching of a coherent spin block confined in a cross-shaped junction of mesoscopic ferromagnetic NiFe wires was probed with the voltage pads attached close (1.5 \ensuremath{\mu}m) to the junction. A positive intrinsic MR effect, i.e., an increase in resistance, associated with local spin noncollinearity, or a 45\ifmmode^\circ\else\textdegree\fi{} domain wall, in a 0.5 \ensuremath{\mu}m cross was demonstrated while the anisotropic MR and the Lorentz MR were unambiguously excluded.

Alternatives to Coscheduling a Network of Workstations

Efficient scheduling of processes on processors of a Network of Workstations (NOW) is essential for good system performance. However, the design of such schedulers is challenging because of the complex interaction between several system and workload parameters. Coscheduling, though desirable, is impractical for such a loosely coupled environment. Two operations, waiting for a message and arrival of a message, can be used to take remedial actions that can guide the behavior of the system toward coscheduling using local information. We present a taxonomy of three possibilities for each of these two operations, leading to a design space of 3×3 scheduling mechanisms. This paper presents an extensive implementation and evaluation exercise in studying these mechanisms. Adhering to the philosophy that scheduling and communication are intertwined and should be studied in conjunction, a complete communication substrate for UltraSPARC workstations, connected by Myrinet and running Solaris 2.5.1, has been developed. This platform provides the entire Message Passing Interface (MPI) to readily run off-the-shelf MPI applications by employing protected low-latency user-level messaging. Several applications can concurrently use this interface. This platform has been used to design, implement, and uniformly evaluate nine scheduling strategies with a mixture of concurrent real applications with varying communication intensities. This includes five new schemes (Periodic Boost, Periodic Boost with Spin Block, Spin Yield, Periodic Boost with Spin Yield, Dynamic Coscheduling with Spin Yield) that are presented in this paper. In addition to our evaluations of the pros and cons of each mechanism in terms of throughput, response time, CPU utilization, and fairness, it is shown that Periodic Boost is a promising approach for scheduling processes on a NOW.

Spin block persistence at finite temperature

We explore a new definition of the persistence exponent, measuring the probability that a spin never flips after a quench of an Ising-like model at a temperature , while the usual definition only makes sense at T = 0. This probability is now defined for spin blocks, and a general scaling for it, involving time and block linear size is introduced and illustrated by extensive simulations.