Transverse Dynamical Structure Factor Research Articles

Magnon peak lineshape in the transverse dynamical structure factor of a ferromagnetically polarized easy-axis XXZ chain at low temperatures

Magnon peak lineshape in the transverse dynamical structure factor of a ferromagnetically polarized easy-axis XXZ chain at low temperatures

Exact solutions of few-magnon problems in the spin- S periodic XXZ chain

We solve few-magnon problems for a finite-size spin-$S$ periodic Heisenberg XXZ chain with single-ion anisotropy through constructing sets of exact Bloch states achieving block diagonalization of the system. Concretely, the two-magnon (three-magnon) problem is converted to a single-particle one on a one-dimensional (two-dimensional) effective lattice whose size depends linearly (quadratically) on the total number of sites. For parameters lying within certain ranges, various types of multimagnon bound states are manifested and shown to correspond to edge states on the effective lattices. In the absence of the single-ion anisotropy, we reveal the condition under which exact zero-energy states emerge. As applications of the formalism, we calculate the transverse dynamic structure factor for a higher-spin chain near saturation magnetization and find signatures of the multimagnon bound states. We also calculate the real-time three-magnon dynamics from certain localized states, which are relevant to cold-atom quantum simulations, by simulating single-particle quantum walks on the effective lattices. This provides a physically transparent interpretation of the observed dynamics in terms of propagation of bound state excitations. Our method can be directly applied to more general spin or itinerant particle systems possessing translational symmetry.

Breathing kagome XY quantum magnet with four-site ring exchange

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a Z2 quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua.

Dynamical spin excitations of the topological Haldane gapped phase in the S=1 Heisenberg antiferromagnetic chain with single-ion anisotropy

We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid similar to a $S=1/2$ Heisenberg antiferromagnetic chain. We further identify that the elementary excitations are fractionalized spinons.

Low-temperature asymptotic of the transverse dynamical structure factor for a magnetically polarized XX chain

The Dyson equation for the real two-time commutator retarded one-magnon Green function of the ferromagnetically polarized XX chain is suggested following the Plakida–Tserkovnikov algorithm. Starting from this result a low-temperature integral representation for the corresponding magnon self-energy is obtained by the truncated form factor expansion, however, without any resummations. Within the suggested approach, the low-temperature asymptotics of the transverse dynamical structure factor may be readily studied. Some obtained line shapes are presented.

Viscoelasticity and dynamical gaps: Rigidity in crystallization and glass-forming liquids

Abstract Rigidity plays an important role on the relaxation properties of glass forming melts, yet it is usually determined from the average coordination number through the chemical composition. A discussion is presented on how viscoelasticity can be used as an alternative way to determine glass rigidity and to give clues about the relaxation processes. It is shown that the transverse current dynamical structure factor of dense glass and crystal forming fluids contain rich information about rigidity that can be related with the presence of a dynamical-gap for transversal vibrational-modes. Then, the number of floppy modes can be related with the dynamical gap size and with the liquid relaxation time. Furthermore, a dynamical average effective coordination number can be defined. Numerical simulations for hard-disks in a dense fluid phase are provided. A discussion is presented on the need to improve glass viscoelasticity models to describe consistently non-exponential stress and strain relaxation.

Elementary excitations in the ordered phase of spin- 12 J1 – J2 model on square lattice

We use recently proposed four-spin bond-operator technique (BOT) to discuss spectral properties of frustrated spin-$\frac12$ $J_1$--$J_2$ Heisenberg antiferromagnet on square lattice at $J_2<0.4J_1$ (i.e., in the N\'eel ordered phase). This formalism is convenient for the consideration of low-lying excitations which appear in conventional approaches as multi-magnon bound states (e.g., the Higgs excitation) because separate bosons describe them in BOT. At $J_2=0$, the obtained magnon spectrum describes accurately available experimental data. However, calculated one-magnon spectral weights and the transverse dynamical structure factor (DSF) do not reproduce experimental findings quantitatively around the momentum ${\bf k}=(\pi,0)$. Then, we do not support the conjecture that the continuum of excitations observed experimentally and numerically near ${\bf k}=(\pi,0)$ is of the Higgs-magnon origin. Upon $J_2$ increasing, one-magnon spectral weights decrease and spectra of high-energy spin-0 and spin-1 excitations move down. One of spin-0 quasiparticles becomes long-lived and its spectrum merges with the magnon spectrum in the most part of the Brillouin zone at $J_2\approx0.3J_1$. We predict that the Higgs excitation and another spin-0 quasiparticle become long-lived around ${\bf k}=(\pi/2,\pi/2)$ at $J_2\agt0.3J_1$ and produce sharp anomalies in the longitudinal DSF.

Z=2 Quantum Critical Dynamics in a Spin Ladder.

By means of inelastic neutron scattering we investigate finite temperature dynamics in the quantum spin ladder compound (C_{5}H_{12}N)_{2}CuBr_{4} (BPCB) near the magnetic field induced quantum critical point with dynamical exponent z=2. We observe universal finite-temperature scaling of the transverse local dynamic structure factor in spectacular quantitative agreement with long-standing theoretical predictions. At the same time, already at rather low temperatures, we observe strong nonuniversal longitudinal fluctuations. To separate the two, we make use of an intrinsic leg-exchange symmetry of the spin ladder. Complementary measurements of specific heat also reveal striking scaling behavior near the quantum critical point.

Dynamical Spin Structure Factors of Anisotropic Spin Ladder in a Longitudinal Magnetic Field

We have addressed the magnetic excitations of quasi-one-dimensional two-leg anisotropic antiferromagnetic spin ladder under the influence of longitudinal magnetic field. Such excitations can be obtained via the study of frequency behavior of dynamical spin structure factors. The original spin model hamiltonian can be transformed to a hard core bosonic gas using a generalized bond operator formalism. We have used the linear response theory within Green’s function approach to obtain the frequency behavior of both longitudinal and transverse dynamical spin structure factor in the gapful regime. The results show energy gap vanishes at critical magnetic field which depends on anisotropic parameters. We have also found the longitudinal spin structure factor shows a sharp single peak at a particular frequency. The position of this peak moves to lower frequencies with increase of both intersite and local anisotropy parameters. However, the effect of intersite anisotropy on the position of peak in the longitudinal structure factor is more remarkable compared to another one. Also the change of magnetic field shows no considerable effect on the behavior of longitudinal spin structure factor. Furthermore, we have studied the dependence of the transverse structure factor on frequency for different magnetic field and anisotropy parameters. Unlike longitudinal case, two separate peaks appears in the transverse spin structure. The enhancement of magnetic field causes that the peaks in the transverse structure factor become far away from each other. Also, the influences of both anisotropies on the spin excitation spectrum of transverse spin components have been discussed.

Finite-temperature scaling of spin correlations in a partially magnetized HeisenbergS=12chain

Inelastic neutron scattering is employed to study transverse spin correlations of a Heisenberg $S=1/2$ chain compound in a magnetic field of 7.5 T. The target compound is the antiferromagnetic Heisenberg $S=1/2$ chain material 2(1,4-Dioxane)$\cdot$2(H$_2$O)$\cdot$CuCl$_2$, or CuDCl for short. The validity and the limitations of the scaling relation for the transverse dynamic structure factor are tested, discussed and compared to the Tomonaga-Luttinger spin liquid theory and to Bethe-ansatz results for the Heisenberg model.

Spin dynamics of the anisotropic spin-1 antiferromagnetic chain at finite magnetic fields

We present results of a study of the antiferromagnetic spin-1 chain, subject to the simultaneous presence of single-ion anisotropy and external magnetic fields. Using quantum Monte-Carlo based on the stochastic series expansion method we first uncover a rich quantum phase diagram comprising N\'eel, Haldane, Luttinger liquid, and large anisotropy phases. Second, we scan across this phase diagram over a wide range of parameters, evaluating the transverse dynamic structure factor, which we show to exhibit sharp massive modes, as well as multi particle continua. For vanishing anisotropy and fields, comparison with existing results from other analytic and numerical approaches shows convincing consistency.

Quasiparticles of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field

Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S+−(κ,ω). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl2·2N(C5D5).

Finite-temperature dynamical structure factor of the Heisenberg-Ising chain

We consider the spin-1/2 Heisenberg $XXZ$ chain in the regime of large Ising-type anisotropy $\ensuremath{\Delta}$. By a combination of duality and Jordan-Wigner transformations we derive a mapping to weakly interacting spinless fermions, which represent domain walls between the two degenerate ground states. We develop a perturbative expansion in $1/\ensuremath{\Delta}$ for the transverse dynamical spin structure factor at finite temperatures and in an applied transverse magnetic field. We present a unified description for both the low-energy temperature-activated response and the temperature evolution of the $T=0$ two-spinon continuum. We find that the two-spinon continuum narrows in energy with increasing temperature. At the same time spectral weight is transferred from the two-spinon continuum to the low-energy intraband scattering continuum, which is strongly peaked around the position of the (single) spinon dispersion (``Villain mode'').

The two-spinon transverse structure factor of the gapped Heisenberg antiferromagneticchain

We consider the transverse dynamical structure factor of the anisotropic Heisenbergspin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime(Δ>1). Specializing to the case of zero field, we use two independent approaches based onintegrability (one valid for finite size, the other for the infinite lattice) to obtain the exacttwo-spinon part of this correlator. We discuss in particular its asymmetry with respect to theπ/2-momentum line, its overall anisotropy dependence, and its contribution to sumrules.

Vibrational behavior of a realistic amorphous-silicon model

The vibrational properties of a high-quality realistic model of amorphous silicon are examined. The longitudinal and transverse dynamical structure factors are calculated, and fitted to a damped harmonic oscillator (DHO) function. The width Γ of the best-fit DHO to the longitudinal dynamical structure factor scales approximately as k 2 for wavevectors k ≲ 0.55 Å −1, which is above the Ioffe–Regel crossover frequency separating the propagating and diffusing regimes, occurring at k = 0.38 ± 0.03 Å −1. Using the DHO function as a fitting function for the transverse dynamical structure factor (without theoretical justification), gives a dependence of Γ ∝ k α with α ∼ 2.5 for wavevectors k ≲ 0.7 Å −1. There was no evidence for Γ ∝ k 4 behavior for either polarization.

1∕S-expansion study of spin waves in a two-dimensional Heisenberg antiferromagnet

We study the effects of quantum fluctuations on excitation spectra in the two-dimensional Heisenberg antiferromagnet by means of the $1∕S$ expansion. We calculate the spin-wave dispersion and the transverse dynamical structure factor up to the second order of $1∕S$ in comparison with inelastic neutron scattering experiments. The spin-wave energy at momentum $(\ensuremath{\pi},0)$ is found to be about 2% smaller than that at $(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ due to the second-order correction. In addition, we study the dimensional crossover from two dimensions to one dimension by weakening exchange couplings in one direction. It is found that the second-order correction becomes large with approaching the quasi-one-dimensional situation and makes the spin-wave energy approach to the des Cloizeaux-Pearson boundary for $S=1∕2$. The transverse dynamical structure factor is also calculated up to the second order of $1∕S$. It is shown that the intensity of the spin-wave peak is strongly reduced while the intensity of three-spin-wave continuum becomes large and exceeds that of the spin-wave peak in the quasi-one-dimensional situation.

Central peak in the Excitation spectra of thin ferroelectric films

The origin of a central peak in the excitation spectra of thin ferroelectric films is ascribed to the relaxation of a surface mode. Contrary to the behavior in bulk materials the central peak appears even far from the phase-transition temperature, where it dominates the energy spectrum. The results are based on an Ising model in a transverse field. Applying a Green's-function formalism the complete transverse dynamic structure factor of ferroelectric thin films is calculated. That structure factor exhibits additional surface mode peaks, the occurrence of which gives rise to a central peak already at low temperatures. The results are in reasonable agreement with experimental data.

Anharmonic effects in LHP- and LDP-type ferroelectrics, investigated with the Green‘s function technique

A Green‘s function technique is used to study the anharmonic pseudo-spin-phonon and phonon-phonon interaction effects in LHP and LDP-type ferroelectrics on optical phonon mode frequency, damping and transverse dynamical structure factor below and above Tc. The coupling between the transverse soft-mode and the optical phonon mode produces a central peak in the transverse dynamical structure factor. The temperature dependence of these quantities is discussed and it is in good agreement with the experimental data. At low temperatures the contribution of the anharmonicity is very small, but at temperatures near the critical temperature Tc and above Tc it increases strongly.

Green function theory of phase transition in CDP-type ferroelectrics

A Green function technique is used to study the effects of spin-optical phonon interactions in the Ising model with a transverse field including interactions within and between the chains of O═H═O bonds. The renormalized energy of the coupled mode, the damping of the spin waves, and the phonon damping are evaluated. The transverse dynamic structure factor exhibits three peaks due to the coupling of the transverse soft-mode and the optical phonon mode. The width of the central peak is proportional to the phonon damping.

Spin‐phonon interactions in the ising model with a transverse field

AbstractA Green function technique is used to study the effects of spin–phonon interactions in the Ising model with a transverse field. The renormalized energy of the coupled mode, the damping of the spin waves, and the phonon damping are evaluated. The transverse dynamic structure factor exhibits three peaks due to the coupling of the transverse soft‐mode and the acoustic phonon mode. The width of the central peak is proportional to the phonon damping.