Infinite Anisotropy Research Articles

Subdiffusive hydrodynamics of nearly integrable anisotropic spin chains

We address spin transport in the easy-axis Heisenberg spin chain subject to different integrability-breaking perturbations. We find subdiffusive spin transport characterized by dynamical exponent z = 4 up to a timescale parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for finite anisotropy, one eventually recovers diffusion at late times but with a diffusion constant independent of the strength of the perturbation and solely fixed by the value of the anisotropy. We provide numerical evidence for these findings, and we show how they can be understood in terms of the dynamical screening of the relevant quasiparticle excitations and effective dynamical constraints. Our results show that the diffusion constant of near-integrable diffusive spin chains is generically not perturbative in the integrability-breaking strength.

Quantum criticality with infinite anisotropy in topological phase transitions between Dirac and Weyl semimetals

We study quantum phase transitions (QPTs) associated with splitting nodal Fermi points, motivated by topological phase transitions between Dirac and Weyl semi-metals. A Dirac point in Dirac semi-metals may be split into two Weyl points by breaking a lattice symmetry or time reversal symmetry, and the Lifshitz transition is commonly used to describe the phase transitions. Here, we show that the Lifshitz description is fundamentally incorrect in QPTs with splitting nodal Fermi points. We argue that correlations between fermions, order parameter, and the long range Coulomb interaction { must} be incorporated from the beginning. One of the most striking correlation effects we find is {\it infinite anisotropy} of physical quantities, which cannot appear in a Lifshitz transition. By using the standard renormalization group (RG) method, two types of infinitely anisotropic quantum criticalities are found in three spatial dimensions varying with the number of the Dirac points ($N_f$). For $N_f = 1$, the ratio of the fermion velocity to the velocity of order parameter excitations becomes universal ($\sqrt{2}-1$) along the Dirac point splitting direction . For $N_f >1$, we find that fermions are parametrically faster than order parameter excitations in all directions. Our RG analysis is fully controlled by the fact that order parameter and fermion fluctuations are at the upper critical dimension, and thus our stable fixed points demonstrate the presence of weakly coupled quantum criticalities with infinite anisotropy.

The effect of magnetic nanoparticle concentration on the structure organisation of a microferrogel

Coarse-grained molecular dynamics simulation is applied to study the structural response of micro-sized magnetopolymer objects – microferrogels (MFG). The results for MFGs with different magnetic properties and concentrations of magnetic filler nanoparticles are analysed to detect the transition between non-aggregated configurations and the states with pronounced chains. The nanoparticles are assumed to be either magnetically isotropic or to possess infinite magnetic anisotropy. It is shown that, depending on the type of the particle anisotropy, an applied field in rather different ways affects the MFG structure and shape. Diagrams describing the degree of aggregation as a function of the parameter of the interparticle magnetodipolar interaction and concentration are presented. In particular, it is found that in the case of infinitely anisotropic nanoparticles the aggregation transitions undergoes via a non-trivial scenario. The effect of the structure transformations on the volume change of the MFG objects is studied as well.

Hořava-Lifshitz bouncing Bianchi IX universes: A dynamical system analysis

We examine the Hamiltonian dynamics of bouncing Bianchi IX cosmologies in Ho\v{r}ava-Lifshitz gravity. The $6$-dim phase space presents two critical points, one asymptotic de Sitter attractor at infinity and a $2$-dim invariant plane. We identified four distinct parameter domains $A$, $B$, $C$ and $D$ for which the pair of critical points engenders distinct features in the dynamics. In the domain $A$ the dynamics consists basically of periodic bouncing orbits, or oscillatory orbits with a finite number of bounces. The center with multiplicity two engenders in its neighborhood the topology of stable and unstable cylinders $R \times S^3$ of orbits. We show that the stable and unstable cylinders coalesce realizing a smooth homoclinic connection to the center manifold, a rare event of regular/non-chaotic dynamics in bouncing Bianchi IX cosmologies. The presence of a saddle of multiplicity two in the domain $B$ engenders a high instability in the dynamics so that the cylinders emerging from the center manifold towards the bounce have four distinct attractors: the center manifold itself, the de Sitter attractor at infinity and two further momentum-dominated attractors with infinite anisotropy. In the domain $C$ we examine the features of invariant manifolds of orbits about a saddle of multiplicity two. The presence of the saddle of multiplicity two engenders bifurcations of the invariant manifold as the energy $E_0$ of the system increases relative to the energy $E_{cr}$ providing structures that were not yet observed in the literature. The domain $D$ is not examined as most of its features are present already in the previous domains.

On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary

This paper concerns with the heat equation in the half-space $\mathbb {R}_{+}^{n}$ with nonlinearity and singular potential on the boundary $\partial \mathbb {R}_{+}^{n}$ . We show a well-posedness result that allows us to consider critical potentials with infinite many singularities and anisotropy. Motivated by potential profiles of interest, the analysis is performed in weak L p -spaces in which we prove linear estimates for some boundary operators arising from the Duhamel integral formulation in $\mathbb {R}_{+}^{n}$ . Moreover, we investigate qualitative properties of solutions like self-similarity, positivity and symmetry around the axis $\overrightarrow {Ox_{n}}$ .

Combinatorial Aspects of Correlation Functions of the XXZ Heisenberg Chain in Limiting Cases

We discuss the connection between quantum integrable models and some aspects of enumerative combinatorics and the theory of partitions. As a basic example, we consider the spin XXZ Heisenberg chain in the limiting cases of zero and infinite anisotropy. The representation of the Bethe wave functions via Schur functions allows us to apply the theory of symmetric functions to calculating the thermal correlation functions as well as the form factors in the determinantal form. We provide a combinatorial interpretation of the correlation functions in terms of nests of self-avoiding lattice paths. The suggested interpretation is in turn related to the enumeration of boxed plane partitions. The asymptotic behavior of the thermal correlation functions is studied in the limit of small temperature provided that the characteristic parameters of the system are large enough. The leading asymptotics of the correlators are found to be proportional to the squared numbers of boxed plane partitions.

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e. by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

Integrable models and combinatorics

Relations between quantum integrable models solvable by the quantum inverse scattering method and some aspects of enumerative combinatorics and partition theory are discussed. The main example is the Heisenberg spin chain in the limit cases of zero or infinite anisotropy. Form factors and some thermal correlation functions are calculated, and it is shown that the resulting form factors in a special -parametrization are the generating functions for plane partitions and self-avoiding lattice paths. The asymptotic behaviour of the correlation functions is studied in the case of a large number of sites and a moderately large number of spin excitations. For sufficiently low temperature a relation is established between the correlation functions and the theory of matrix integrals. Bibliography: 125 titles.

Interplay between effective mass anisotropy and Pauli paramagnetic effects in a multiband superconductor: Application toSr2RuO4

We investigate the mixed state properties in a type II multiband superconductor with uniaxial anisotropy under the Pauli paramagnetic effects. Eilenberger theory extended to a multiband superconductor is utilized to describe the detailed vortex lattice properties, such as the flux line form factors, the vortex lattice anisotropy and magnetic torques. We apply this theory to Sr$_2$RuO$_4$ to analyze those physical quantities obtained experimentally, focusing on the interplay between the strong two-dimensional anisotropy and the Pauli paramagnetic effects. This study allows us to understand the origin of the disparity between the vortex lattice anisotropy ($\sim$60) and the $H_{\rm c2}$ anisotropy ($\sim$20). Among the three bands; $\gamma$ with the effective mass anisotropy $\sim$180, $\alpha$ with $\sim$120, and $\beta$ with $\sim$60, the last one is found to be the major band, responsible for various magnetic responses while the minor $\gamma$ band plays an important role in the vortex formation. Namely, in a field orientation slightly tilted away from the two dimensional basal plane those two bands cooperatively form the optimal vortex anisotropy which exceeds that given by the effective mass formula with infinite anisotropy. This is observed by small angle neutron scattering experiments on Sr$_2$RuO$_4$. The pairing symmetry of Sr$_2$RuO$_4$ realized is either spin singlet or spin triplet with the d-vector strongly locked in the basal plane. The gap structure is that the major $\beta$ band has a full gap and the minor $\gamma$ band has a $d_{x^2-y^2}$ like gap.

Coexistence of diffusive and ballistic transport in a simple spin ladder.

We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the transport is found to be diffusive. This shows that (i)quantum chaotic systems can possess ballistic subspaces, and (ii)diffusive and ballistic transport modes can coexist in a rather simple nonintegrable model. In the limit of an infinite anisotropy in rungs the system studied is equivalent to the one-dimensional Hubbard model.

Routing of Deep‐Subwavelength Optical Beams and Images without Reflection and Diffraction Using Infinitely Anisotropic Metamaterials

Interfaces between media with infinite anisotropy, defined by infinite permittivity or permeability in one direction, offer new opportunities for controlling and manipulating light at the nanoscale. Reflectionless, diffraction-free routing of deep-subwavelength optical beams and images using interfaces between infinitely anisotropic media are demonstrated. It is shown how to achieve extremely large anisotropy using metamaterial designs that can be implemented with existing materials.

Engelund’s Two-Dimensional Drainage Equation for a Toe-Drain and the Dupuit-Forchheimer Drainage Equation for a Ditch: A Coincidental Match

Water-table heights attributable to steady uniform surface accretion rates in drained lands overlying a horizontal impermeable bed are given analytically by Engelund’s solution for toe-drains and by the approximate Dupuit-Forchheimer analysis for ditch drains. Both give the same water tables, although for different types of drain, when the spacing of the ditches in the latter is taken to be that in which the water table is drawn down to the level of the toe-drain in Engelund’s derivation. This fortuitous match also occurs in anisotropic soils when the horizontal hydraulic conductivity component is used in the formulae with the drain spacing dependent on the anisotropy factor. For soils with an infinite anisotropy factor, the Dupuit-Forchheimer analysis is exact so that the match is no longer fortuitous.

The correlation functions of the $XXZ$ Heisenberg chain in the case of zero or infinite anisotropy, and random walks of vicious walkers

The XXZ Heisenberg chain is considered for two specific limits of the anisotropy parameter: $\Dl\to 0$ and $\Dl\to -\infty$. The corresponding wave functions are expressed by means of the symmetric Schur functions. Certain expectation values and thermal correlation functions of the ferromagnetic string operators are calculated over the base of N-particle Bethe states. The thermal correlator of the ferromagnetic string is expressed through the generating function of the lattice paths of random walks of vicious walkers. A relationship between the expectation values obtained and the generating functions of strict plane partitions in a box is discussed. Asymptotic estimate of the thermal correlator of the ferromagnetic string is obtained in the limit of zero temperature. It is shown that its amplitude is related to the number of plane partitions.

Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior

The overall behavior of a two-dimensional lattice of voids embedded in an anisotropic elastic matrix is investigated in the limit of vanishing porosity $f$. An effective-medium model (of the Clausius-Mossoti type), which accounts for elastic interactions between neighboring voids, is compared to fast Fourier transform numerical solutions and, in the limits of infinite anisotropy, to exact results. A crossover between regular and singular dilute regimes is found, driven by a characteristic length which depends on $f$ and on the anisotropy strength. The singular regime, where the leading dilute correction to the elastic moduli is an $O({f}^{1/2})$, is related to strain localization and to change in character---from elliptic to hyperbolic---of the governing equations.

Dielectric and piezoelectric properties of sol–gel derived Ca doped PbTiO 3

Synthesis of Ca doped PbTiO 3 powder by a chemically derived sol–gel process is described. Crystallization characteristics of different compositions Pb 1− x Ca x TiO 3 (PCT) with varying calcium (Ca) content in the range x = 0–0.45 has been investigated by DTA/TGA, X-ray diffraction and scanning electron microscopy. The crystallization temperature is found to decrease with increasing calcium content. X-ray diffraction reveals a tetragonal structure for PCT compositions with x ≤ 0.35, and a cubic structure for x = 0.45. Dielectric properties on sintered ceramics prepared with fine sol–gel derived powders have been measured. The dielectric constant is found to increase with increasing Ca content, and the dielectric loss decreases continuously. Sol–gel derived Pb 1− x Ca x TiO 3 ceramics with x = 0.45 after poling exhibit infinite electromechanical anisotropy ( k t/ k p) with a high d 33 = 80 pC/N, ɛ′ = 298 and low dielectric loss (tan δ = 0.0041).

Flux melting inBi2Sr2CaCu2O8+δ: Incorporating both electromagnetic and Josephson couplings

Multilevel Monte Carlo simulations of a BSCCO system are carried out including both Josephson as well as electromagnetic couplings for a range of anisotropies. A first order melting transition of the flux lattice is seen on increasing the temperature and/or the magnetic field. The phase diagram for BSCCO is obtained for different values of the anisotropy parameter $\gamma$. The best fit to the experimental results of D. Majer {\it et al.} [Phys. Rev. Lett. {\bf 75}, 1166 (1995)] is obtained for $\gamma\approx 250$ provided one assumes a temperature dependence $\lambda^2(0)/\lambda^2(T)=1-t$ of the penetration depth with $t=T/T_c$. Assuming a dependence $\lambda^2(0)/\lambda^2(T)=1-t^2$ the best fit is obtained for $ \gamma\approx 450$. For finite anisotropy the data is shown to collapse on a straight line when plotted in dimensionless units which shows that the melting transition can be satisfied with a single Lindemann parameter whose value is about 0.3. A different scaling applies to the $\gamma=\infty$ case. The energy jump is measured across the transition and for large values of $\gamma$ it is found to increase with increasing anisotropy and to decrease with increasing magnetic field. For infinite anisotropy we see a 2D behavior of flux droplets with a transition taking place at a temperature independent of the magnetic field. We also show that for smaller values of anisotropy it is reasonable to replace the electromagnetic coupling with an in-plane interaction represented by a Bessel function of the second kind ($K_0$), thus justifying our claim in a previous paper.

AXIAL AND OFF-AXIAL DYNAMIC TRANSITIONS IN UNIAXIALLY ANISOTROPIC HEISENBERG FERROMAGNET: A COMPARISON

Uniaxially anisotropic Heisenberg ferromagnet, in the presence of a magnetic field varying sinusoidally in time, is studied by Monte Carlo simulation. The axial (field applied only along the direction of anisotropy) and off-axial (field applied only along the direction which is perpendicular to the direction of anisotropy) dynamic transitions are studied. By studying the distribution of the dynamic order parameter component, it is observed that the axial transition is discontinuous for low anisotropy and becomes continuous in high anisotropy. The off-axial transition is found to be continuous for all values of anisotropy. In the infinite anisotropy limit, both types of transitions are compared with that observed in an Ising ferromagnet for the same value of the field and frequency. The infinitely anisotropic axial transition and dynamic transition in the Ising ferromagnet occur at different temperatures, whereas the infinitely anisotropic off-axial transition and the equilibrium ferro-para transition in the Ising model occur at the same temperature.

Hysteresis and avalanches in the random anisotropy Ising model

The behavior of the random anisotropy Ising model at $T=0$ under local relaxation dynamics is studied. The model includes a dominant short-range ferromagnetic interaction and assumes an infinite anisotropy at each site along local anisotropy axes which are randomly aligned. As a consequence, some of the effective interactions become antiferromagneticlike and frustration appears. Two different random distributions of anisotropy axes have been studied. Both are characterized by a parameter that allows control of the degree of disorder in the system. By using numerical simulations we analyze the hysteresis loop properties and characterize the statistical distribution of avalanches occurring during the metastable evolution of the system driven by an external field. A disorder-induced critical point is found in which the hysteresis loop changes from displaying a typical ferromagnetic magnetization jump (large avalanche spanning a macroscopic fraction of the system) to a rather smooth loop exhibiting only tiny avalanches. The critical point is characterized by a set of critical exponents, which are consistent with the universal values proposed from the study of other simpler models.

Infinite anisotropy of the piezoeffect in PbTiO3-based ferroceramic

Acoustic emission, dilatometry, and optical microscopy were used to study the polarization of PKR-70 PbTiO3 ferroceramic samples. It was established that in an electric field higher than 2.5 kV/mm the piezoeffect in the samples acquires an infinite anisotropy, accompanied by acoustic-emission and dilatometric anomalies. It is shown that this anisotropy of the piezoeffect is caused by microcracking of the samples in the direction of the polarizing field.

Magnetization switching in small ferromagnetic particles: Nucleation and coherent rotation

The mechanisms of thermally activated magnetization switching in small ferromagnetic particles driven by an external magnetic field are investigated. For low uniaxial anisotropy the spins rotate coherently while for sufficiently large uniaxial anisotropy they behave Ising-like, i.e., the switching then is due to nucleation. The crossover from coherent rotation to nucleation is studied for the classical three-dimensional Heisenberg model with uniaxial anisotropy by Monte Carlo simulations. From the temperature dependence of the metastable lifetime the energy barrier of a switching process can be determined. For the case of infinite anisotropy we compare numerical results from simulations of the Ising model with theoretical results for energy barriers for both, single- and multidroplet nucleation. The simulated barriers are in agreement with the theoretical predictions.