Dynamic Spin Correlation Function Research Articles

Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

Theoretical scheme for finite-temperature dynamics of Kitaev’s spin liquids

In this article, we review the theoretical formulation of finite temperature dynamics of Kitaev’s spin liquid. We present the exact analytical solution of the dynamical spin correlation function at the integrable limit of Kitaev’s model, on the basis of (2018 Phys. Rev. B 98 220404). By combining the analytical solution with the equilibrium classical Monte-Carlo scheme, we construct a formulation to access the finite temperature dynamics of Kitaev’s spin liquid exactly, with a reasonable amount of computational cost. This formulation is based on the real-time representation, which enables us to directly access the experimental observables defined in real frequency, without analytical continuation. The real-time scheme is essential to capturing the resonant features of the spectrum accurately, which occurs e.g. in the chiral spin liquid phase with isolated Majorana zero modes. Accordingly, this scheme provides an effective approach to address the nature of fractional excitations in Kitaev’s spin liquid. As an application, we address the detection of zero mode around the site vacancy through the local resonant spectrum and discuss how the character of Kitaev’s spin liquid emerges in its dynamical signature.

Growth kinetics of the two-dimensional Ising model with finite cooling rates.

We investigate, via spin-flip kinetic Monte Carlo simulations, the entire growth kinetic process of the two-dimensional kinetic Ising model cooled to zero temperature with finite cooling rates. A new slow dynamics, suppressed, and unseen in the instantaneous quench emerges and eventually crosses over to the asymptotic standard coarsening behavior. We present a numerical observation of the excess defect number density that provides direct information on the generated defects due to the critical slowing down. We find that the excess defect density reveals the dynamics of defect generation, which is shown to be in good agreement with the scaling theory pioneered by Kibble and Zurek (KZ). The dynamic spin correlation function reveals that the impulse regime alluded by KZ is characterized by a unique critical coarsening process with the growth law dictated by the Kibble-Zurek mechanism. We determine a new dynamic exponent governing the growth kinetics at the onset times of the zero temperature. The proposed scaling scheme for the excess defect density leads to an analytic expression for this dynamic exponent involving the KZ exponents, indicating the extended influence of the KZ mechanism even down to the kinetics at the onset times of zero temperature. We also perform dynamic simulations of critical heating with finite rates from zero temperature where the power law relaxation (with respect to the inverse cooling rates) of the magnetization can be explained clearly by the KZ exponent.

Vison-Majorana complex zero-energy resonance in the Kitaev spin liquid

We study the effect of site dilution in Kitaev's model. We derive an analytical solution of the dynamical spin correlation functions for arbitrary configurations of $Z_2$ fluxes. By incorporating this solution into classical Monte Carlo scheme, we address how a site vacancy affects the experimental observables, such as the static spin susceptibility and the spin lattice relaxation rate, $1/T_1$. As a result, we found an enhancement of dynamical magnetic response in the vicinity of vacancy, which leads to Friedel-like oscillation in local $1/T_1$, in contrast to limited influences on the static susceptibility. Furthermore, we found a sharp zero-energy peak in the magnetic excitation spectrum, which is attributed to the Vison & Majorana zero mode trapped near the site vacancy. This zero mode can be interpreted as fractionalized spin hole into an Ising triplet with differentiated magnetic axes, which leads to the characteristic temperature and field-orientational dependence of $1/T_1$.

Finite-temperature phase transition to a quantum spin liquid in a three-dimensional Kitaev model on a hyperhoneycomb lattice

We present numerical evidence for the presence of a finite-temperature ($T$) phase transition separating paramagnet and quantum spin liquid in a three-dimensional variant of the Kitaev model defined on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from quantum spin liquid to paramagnet at a finite critical temperature $T_c$. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above $T_c$, while it obeys the Curie law at high $T$ and approaches a nonzero Van Vleck-type constant at low $T$. Although the susceptibility changes continuously at $T_c$, its $T$ derivative shows critical divergence at $T_c$. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to the discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables as well as the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition is interpreted as the one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. A correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently-discovered hyperhoneycomb compound, $\beta$-Li$_2$IrO$_3$, is mentioned.

Absolute cross-section normalization of magnetic neutron scattering data

We discuss various methods to obtain the resolution volume for neutron scattering experiments, in order to perform absolute normalization on inelastic magnetic neutron scattering data. Examples from previous experiments are given. We also try to provide clear definitions of a number of physical quantities which are commonly used to describe neutron magnetic scattering results, including the dynamic spin correlation function and the imaginary part of the dynamic susceptibility. Formulas that can be used for general purposes are provided and the advantages of the different normalization processes are discussed.

Effects of frustration on magnetic excitations in a two-leg spin-ladder system

We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearestneighbor bonds in the leg direction, and on the nearest-neighbor bonds in the rung direction. A dynamical spin correlation function at zero temperature is calculated by using the dynamical density-matrix renormalization-group method for possible magnetic phases, i.e., columnar-dimer and rung-singlet phases. The columnar-dimer phase is characterized by multi-spinon excitations with spin gap, while the rung-singlet phase is dominated by the triplet excitation in the rung direction. It is found that a major difference between these two phases appears in the spectral weight of magnetic excitations, in particular, of the bonding and anti-bonding modes in the rung direction. Therefore, we can distinguish one phase from the other by the difference of the spectral weight. Furthermore, we examine frustration effect on both modes in the rung-singlet phase with a perturbation theory from the strong coupling limit. It is shown that the anti-bonding mode is stable against the frustration, and a wavenumber with minimum excitation energy is shifted from the commensurate to incommensurate ones. On the other hand, the bonding mode is merged into the continuum excitation of multiple triplet excitations by increasing the frustration. By comparing our results with inelastic neutron scattering experiments for BiCu$_2$PO$_6$, the magnitude of the magnetic exchange interactions and the ground state will be determined.

Magnetic Excitation in Interacting Spin Trimer Systems Investigated by Extended Spin-Wave Theory

Magnetic property of interacting spin trimer systems is studied theoretically focussing on (C 5 H 11 NO 2 ) 2 ·3CuCl 2 ·2H 2 O as a typical example, where the trimer is composed of three S =1/2 spins. It is reported that (C 5 H 11 NO 2 ) 2 ·3CuCl 2 ·2H 2 O has low-field and high-field magnetically ordered phases at low temperatures, where the two phases are separated by a 1/3 magnetization plateau region. The quantum phase transition and magnetic excitation are investigated on the basis of an extended spin-wave theory which was developed in studying interacting spin dimer systems. Formulation of dynamical spin correlation function is presented by introducing form factors for trimers with which interference effects inside the trimer can be taken into account appropriately. Introducing the form factors enables us to treat a trimer as a kind of an atom and makes the formulation simple. Magnetic excitations are classified with transverse and longitudinal modes. It is found that each mode is characterized by i...

Existence of staggered fields in the Ising-like antiferromagnetic compounds CsCoCl3 and CsCoBr3

The line shapes of dynamical spin correlation functions of the Ising-like antiferromagnetic compounds, CsCoCl3 and CsCoBr3, show asymmetry about its peak positions in which the spectral weights mainly concentrate in the low energy side. We consider a one-dimensional Ising-like S=12 Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in the presence of a staggered magnetic field hx along the transverse direction in order to explain those asymmetric line shapes. We obtain dynamical spin correlation functions along the magnetic field Sxx(q,ω) and perpendicular to it Syy(q,ω). It is shown that the line shapes of Sxx(q,ω) and Syy(q,ω) are highly asymmetric at all values of q and hx. An excellent agreement with the experimental data throughout the whole Brillouin zone is observed upon considering a finite value of the staggered fields for both the compounds CsCoCl3 and CsCoBr3. The existence of staggered fields is justified by considering the zigzag orientations of the nonmagnetic atoms about the magnetic Co atoms.

The two-component spin–fermion model for high-Tc cuprates: its applications in neutron scattering and ARPES experiments

Motivated by neutron scattering experiments in high-Tc cuprates, we propose the two-component spin–fermion model as a minimal phenomenological model, which has both local spins and itinerant fermions as independent degrees of freedom (d.o.f.). Our calculations of the dynamic spin correlation function provide a successful description of the puzzling neutron experiment data and show that: (i) the upward dispersion branch of magnetic excitations is mostly due to local spin excitations; (ii) the downward dispersion branch is from collective particle–hole excitations of fermions; and (iii) the resonance mode is a mixture of both d.o.f. Using the same model with the same set of parameters, we calculated the renormalized quasiparticle (q.p.) dispersion and successfully reproduced one of the key features of the angle-resolved photoemission spectroscopy (ARPES) experiments, namely the high-energy kink structure in the fermion q.p. dispersion, thus supporting the two-component spin–fermion phenomenology.

Spin Excitation Assisted by Non-Softening Phonon for Spin-Peierls Model

We study spin dynamics of a spin-Peierls chain with nearest-neighbor and next-nearest-neighbor Heisenberg spin exchange interactions together with a gapped and dispersionless phonon. The dynamical spin correlation function and phonon excitation spectrum are calculated at zero temperature by using dynamical density-matrix renormalization-group method. We find a new spin excitation assisted by non-softening phonon. The excitation is located above phonon in energy and shows a dispersive feature with strong intensity near the momentum π. The phonon excitation spectrum is also influenced by the spin–phonon interaction. We discuss the possibility of observing the spin–phonon coupled features in inorganic spin-Peierls compound CuGeO 3 .

The two-time Green’s function and the diagram technique

Based on constructing the equations of motion for the two-time Green’s functions, we discuss calculating the dynamical spin susceptibility and correlation functions in the Heisenberg model. Using a Mori-type projection, we derive an exact Dyson equation with the self-energy operator in the form of a multiparticle Green’s function. Calculating the self-energy operator in the mode-coupling approximation in the ferromagnetic phase, we reproduce the results of the temperature diagram technique, including the correct formula for low-temperature magnetization. We also consider calculating the spin fluctuation spectrum in the paramagnetic phase in the framework of the method of equations of motion for the relaxation function.

Domain wall dynamics of the spin- $\frac{1}{2}$ Ising-like antiferromagnetic chain in presence of Dzyaloshinskii-Moriya interactions

We consider a one-dimensional Ising-like S = $\frac{1}{2}$ Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in presence of both uniform and staggered Dzyaloshinskii-Moriya interactions. We obtain dispersion relations and dynamical spin correlation functions, S x x (q, ω) using the basis of domain wall pair states. It is shown that the line shapes of S x x (q, ω) are highly asymmetric over the whole Brillouin zone such that the spectral weights mainly concentrate in the low energy side. It is observed that presence of staggered Dzyaloshinskii-Moriya interaction explains the experimental results on the Ising-like antiferromagnetic compounds CsCoCl3 and CsCoBr3 very well.

Power-Law Spin Correlations in a Perturbed Spin Model on a Honeycomb Lattice

We consider the spin-1/2 model on the honeycomb lattice in the presence of a weak magnetic field hα << 1. Such a perturbation destroys the exact integrability of the model in terms of gapless fermions and static Z2 fluxes. We show that it results in the appearance of a long-range tail in the irreducible dynamic spin correlation function: <<s(z)(t,r)s(z)(0,0)>> ∝ h(z)(2)f(t,r), where f(t,r) ∝ [max(t,r)]-4 is proportional to the density polarization function of fermions.

Transverse and Longitudinal Excitation Modes in Interacting Multispin Systems

Magnetic excitation in coupled multispin system is studied theoretically focusing on Cu 2 Fe 2 Ge 4 O 13 and Cu 2 CdB 2 O 6 as typical examples of such system. These compounds consist of spin dimer and spin monomer parts and show an antiferromagnetic phase transition at low temperatures due to the spin monomer part. A multispin containing a spin dimer and spin monomers is treated as a basis unit. The multispin forms a spin multiplet and its energy levels are separated into high and low regions reflecting the characteristic energies of the dimer and monomer parts. We regard the system as interacting multispins and apply an extended Holstein–Primakoff theory by introducing bosons for each energy level of a spin multiplet. In the low-energy region, the obtained magnon dispersion and dynamical spin correlation function agree quantitatively with experimental results of inelastic neutron scattering performed in Cu 2 Fe 2 Ge 4 O 13 . Analyzing dynamical spin correlation functions, we find several high-energy modes with longitudinal spin fluctuations peculiar to the coupled spin dimer and spin monomer system. One-magnon Raman scattering is studied to probe such longitudinal modes. Magnetic excitation in Cu 2 CdB 2 O 6 is also studied in the same way.

Theory of magnetic excitation for coupled spin dimer and spin chain system Cu2Fe2Ge4O13

Cu2Fe2Ge4O13 is a quantum magnet consisting of Cu spin dimers and Fe spin chains. It shows an antiferromagnetic phase transition at low temperatures due to the magnetic moment of Fe. Since the two parts are weakly coupled, magnetic excitations are well separated into high-energy Cu dimer part and low-energy Fe chain part. We study the magnetic excitations in the ordered phase of Cu2Fe2Ge4O13 based on a theory used for coupled spin dimer systems such as TlCuCl3. Analyzing the dynamical spin correlation functions, we find several high-energy modes with longitudinal spin fluctuations peculiar to the coupled spin dimer and spin chain system. This is consistent with the recent experimental result of inelastic neutron scattering. A possibility to detect such longitudinal modes is discussed by means of magnetic Raman scattering.

Exact diagonalization study of the antiferromagnetic spin-12Heisenberg model on the square lattice in a magnetic field

We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In the first part, we calculate the spin-wave velocity c, the spin stiffness rho(s), and the magnetic susceptibility chi(perpendicular to), and thus determine the microscopic parameters of the low-energy long-wavelength description. In the second part, we present a comprehensive study of dynamical spin-correlation functions for magnetic fields ranging from zero up to saturation. We find that, at low fields, magnons are well defined in the whole Brillouin zone but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multimagnon scattering. Our results directly apply to inelastic neutron-scattering experiments.

Theory of magnetic excitations in high-Tc cuprates: Two component spin-fermion model

Recent neutron scattering experiments have revealed that the generic form of the magnetic excitations in the high-Tc cuprates has the so-called "hourglass" shape; it features both upward and downward excitations at the incommensurate (IC) momenta merging to the resonance peak at the commensurate momentum (π,π). We propose the two-component spin-fermion model as a minimal phenomenological model which has both local spins and itinerant fermions as independent degrees of freedom. Our calculations of the dynamic spin correlation function provide good agreement with experiments and show: (1) the upward dispersion branch of magnetic excitations is mostly due to the local spin excitations; (2) the downward dispersion branch is from collective spin excitations of fermions; (3) the resonance mode is a mixture of both degrees of freedom.

Integral equations and long-time asymptotics for finite-temperature Ising chain correlationfunctions

This work concerns the dynamical two-point spin correlation functions of the transverseIsing quantum chain at finite (non-zero) temperature, in the universal region near thequantum critical point. They are correlation functions of twist fields in the massiveMajorana fermion quantum field theory. At finite temperature, these are known to satisfy aset of integrable partial differential equations, including the sinh–Gordon equation. Weapply the classical inverse scattering method to study them, finding that the ‘initialscattering data’ corresponding to the correlation functions are simply related to theone-particle finite-temperature form factors calculated recently by one of the persentauthors. The set of linear integral equations (Gelfand–Levitan–Marchenko equations)associated with the inverse scattering problem then gives, in principle, the two-pointfunctions at all space and time separations, and all temperatures. From these, we evaluatethe long-time asymptotic expansion ‘near the light cone’, in the region where thedifference between the space and time separations is of the order of the correlationlength.

Soliton contribution to the electron paramagnetic resonance linewidth in a two-dimensionalantiferromagnet with a staggered field

In this paper we study the interactions between magnons and a solitonin a classical and isotropic two-dimensional Heisenberg antiferromagnetin the presence of a staggered field applied perpendicularly to theXY plane. The temperature dependence of the linewidth is calculated using the dynamic spincorrelation function derived from soliton–magnon scattering.