Dynamic Spin Correlation Function Research Articles

Exact Results for Spin Dynamics and Fractionalization in the Kitaev Model

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in nontrivial quantum spin models. The result is also novel: in spite of the presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation. This shows existence of a gapless but short range spin liquid. An unusual, all energy scale fractionalization of a spin-flip quanta, into two infinitely massive pi fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.

Mott Transition in Kagomé Lattice Hubbard Model

We investigate the Mott transition in the kagomé lattice Hubbard model using a cluster extension of dynamical mean field theory. The calculation of the double occupancy, the density of states, and the static and dynamical spin correlation functions demonstrates that the system undergoes the first-order Mott transition at the Hubbard interaction U/W approximately 1.4 (W:bandwidth). In the metallic phase close to the Mott transition, we find the strong renormalization of three distinct bands, giving rise to the formation of heavy quasiparticles with strong frustrated interactions. It is elucidated that the quasiparticle states exhibit anomalous behavior in the temperature-dependent spin correlation functions.

Effects of disorder in two-dimensional quantum antiferromagnets

We study the effects of disorder in two-dimensional quantum antiferromagnets on a square lattice, within the nonlinear sigma model approach, by using a random continuum distribution of spin stiffnesses or zero-temperature spin gaps, respectively, in the renormalized classical and quantum disordered phases. The quenched staggered magnetic susceptibility at low temperatures is evaluated in each case, showing that the phase structure of the clean system is preserved. The asymptotic behavior of the quenched static and dynamic spin correlation functions is also obtained in the quantum disordered phase. Disorder is shown to introduce a change from exponential to power-law decay in these functions, indicating that the spin excitations become gapless, in spite of the fact that the system is in a paramagnetic state. The scale determining the change in behavior is related to the variance of the distribution function. A comparison is made with the dual behavior of skyrmion topological excitations in the renormalized classical phase. The effect found here is compared with the one produced by Griffiths singularities occurring in disordered systems.

Magnetic properties of a Kondo insulator with RKKY interaction: extended dynamicalmean field study

We study the Kondo lattice model with the Heisenberg-type RKKY exchange couplingamong localized f spins in the presence of a magnetic field. By means of an extendeddynamical mean field theory combined with the non-crossing approximation, we investigatethe one-particle spectral function and the dynamical spin correlation function in the Kondoinsulating phase. It is shown that the magnetic field and the RKKY exchange interactionboth cause instability to the antiferromagnetic order with enhanced transverse spinfluctuations, which give rise to a strong renormalization of quasi-particles as the systemapproaches the quantum critical point. This leads to a tendency to retain the Kondoinsulating gap up to rather large fields.

Dynamical domain walls and spin-Peierls order in doped antiferromagnets: Evidence from exact diagonalization of small clusters

The hole-doped two-dimensional(2D) $t\ensuremath{-}J$ model is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster which, unlike the standard tilted-square clusters, can in principle accomodate an antiphase domain wall. For hole concentration $10%$ and $J/t>~0.5$ the ground-state energy/site is lower than the conventional tilted-square $\sqrt{20}\ifmmode\times\else\texttimes\fi{}\sqrt{20}$ cluster. In the ground state two holes form a loosely bound pair pinned to an antiphase domain wall. The dynamical density correlation function shows sharp quasiparticlelike peaks, reminiscent of the ``holons'' in 1D chains, which suggest the existence of solitonlike propagating domain walls. The dynamical correlation function of the bond-singlet operator has a low-energy peak structure characteristic of columnar spin-Peierls order, the dynamical spin-correlation function shows an intense and isolated ``resonance peak'' near $(\ensuremath{\pi},\ensuremath{\pi}).$

Extended quantum critical phase in a magnetized spin-1/2 antiferromagnetic chain.

Measurements are reported of the magnetic field dependence of excitations in the quantum critical state of the spin S=1/2 linear chain Heisenberg antiferromagnet copper pyrazine dinitrate (CuPzN). The complete spectrum was measured at k(B)T/J< or =0.025 for H=0 and H=8.7 T, where the system is approximately 30% magnetized. At H=0, the results are in agreement with exact calculations of the dynamic spin correlation function for a two-spinon continuum. At H=8.7 T, there are multiple overlapping continua with incommensurate soft modes. The boundaries of these continua confirm long-standing predictions, and the intensities are consistent with exact diagonalization and Bethe ansatz calculations.

Critical magnetic scattering in invar Fe 65 Ni 35 alloy

A critical small angle polarized neutron scattering experiment on invar Fe65Ni35 alloy was performed in the magnetic field H of value from 10 to 1000 G using a special ‘inclined’ geometry (H is inclined to the wave vector k). Two contributions to the critical scattering were studied in the temperature range TC±0.1TC: first, the two-spin correlation function with its amplitude and the correlation length RC(T,H ) and, second, the three-spin dynamical spin-correlation function, by extracting an asymmetric part of the polarization-dependent scattering. The data are interpreted in terms of static and dynamic scaling theory.

Calculation of local magnetic characteristics of ferromagnetic metals taking into account the dynamic spin fluctuations

The numerical calculations of the transverse and longitudinal susceptibilities, the dynamic spin correlation function and the local magnetic moment of ferromagnetic metals are performed taking into account the real band structure and dynamic spin fluctuations. A good agreement between theory and experiments on magnetovolume effect and neutron scattering has been found.

Spin and charge response to magnetic frustration in strongly correlated itinerant electron systems

We investigate the effects of magnetic frustration on spin and charge dynamics in strongly correlated itinerant electron systems by using the exact diagonalization technique. A Hubbard model with adjustable degree of magnetic frustration is constructed. Static and dynamic spin and charge correlation functions show different dependence on the degree of magnetic frustration in the system. With increasing magnetic frustration, the spin and charge correlation function spectra become more sparse, indicating a decreased level of mixing of the spin and charge degrees of freedom or a partial spin-charge separation.

Effect of four-spin interaction on magnetic excitation in ladder and 2D insulating cuprates

We investigate the effect of the cyclic four-spin interaction J cyc on the magnetic excitation spectra in two-leg ladder and two-dimensional (2D) insulating cuprates. The dynamical spin-correlation function S( q, ω) is calculated by using the numerically exact diagonalization method. For the ladder system, we find that the dispersion of spin wave along momentum q =(0, π) to (π/2,π) flattens by introducing J cyc. This feature is consistent with the experimental results of recent inelastic neutron-scattering measurement. For the 2D system, we find that the J cyc reduces effectively the magnetic interactions between nearest-neighbor (NN) Cu spins by about 20%. Moreover, it is found that the dispersion along the magnetic zone boundary from q =( π,0) to (π/2,π/2) has a finite width. This behavior can be understood by considering that the J cyc gives effectively a ferromagnetic diagonal interaction between next NN Cu spins. In order to verify the effect of J cyc, the inelastic neutron-scattering experiment at high-energy region will be highly desirable for 2D cuprates.

Dynamical Properties of the 1/r2-Type Supersymmetrict-JModel in a Magnetic Field: Manifestation of Spin-Charge Separation

Quasi-particle picture in a magnetic field is pursued for dynamical spin and charge correlation functions of the one-dimensional supersymmetric t-J model with inverse-square interaction. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of relevant excited states are identified which are valid in the thermodynamic limit. The excitation contents are composed of spinons, antispinons, holons and antiholons obeying fractional statistics. Both longitudinal and transverse components of the dynamical spin structure factor are independent of the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. The dynamical charge structure factor does not depend on the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. These features indicate the strong spin-charge separation in dynamics, reflecting the high symmetry of the model.

Exact dynamics in the Haldane–Shastry spin chain model in magnetic field

Dynamical spin correlation function S zz(Q, ω) with Q smaller than π m ̄ ( m̄ being magnetization) is derived exactly for the spin chain with the 1/ r 2 interaction in magnetic field. It is found that only two spinons and one antispinon contribute to S zz(Q, ω) in the thermodynamic limit. In deriving the result we use the solution of the Sutherland model with internal symmetry in the strong coupling limit. Our theory keeps the full symmetry of the model in contrast to the previous one which is based on mapping onto the single-component Sutherland model.

Dynamics of the t– J model in a magnetic field

Quasi-particle picture is pursued for dynamical charge and spin correlation functions of the one-dimensional supersymmetric t– J model with inverse-square interaction in a magnetic field. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of intermediate states are identified in the thermodynamic limit. The dynamical charge structure factor is independent of the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. The spin dynamics do not depend on the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. These features indicate the strong spin–charge separation in dynamics, reflecting the high symmetry of the model.

Fluctuation effects of nonlinear coupling between spin and charge excitations on dynamical correlation functions of the one-dimensional extended Hubbard model

We study fluctuation effects of nonlinear coupling between spin and charge excitations on dynamical correlation functions of the one-dimensional extended Hubbard model at half-filling. Two kinds of dynamical correlation functions, dynamical spin- and charge-correlation functions, are calculated by means of a quantum Monte Carlo simulation. We show that the dynamical spin-correlation function has a new peak on the high-energy side of the well-known magnon peak. Since this peak always appears above the charge-excitation gap, it should originate from a charge fluctuation induced through a final-state interaction of magnon creation. We also show that in the dynamical charge-correlation function, a charge-transfer excitation peak is broadened by fluctuation effects due to magnons. These results clearly show that spin and charge excitations are nonlinearly coupled in this system.

Critical dynamics of a uniaxial and dipolar ferromagnet

We study the critical dynamics of three-dimensional ferromagnets with uniaxial anisotropy by taking into account exchange and dipole-dipole interaction. The dynamic spin correlation functions and the transport coefficients are calculated within a mode coupling theory. It is found that the crossover scenario is determined by the subtle interplay between three length scales: the correlation length, the dipolar and uniaxial wave vector. We compare our theoretical findings with hyperfine interaction experiments on Gd and find quantitative agreement. This analysis allows us to identify the universality class for Gd. It also turns out that the $\mu$SR relaxation rate can be best fitted if it is assumed that muons occupy octahedral interstitials sites within the Gd lattice.

Interchain interactions and magnetic properties ofLi2CuO2

An effective Hamiltonian is constructed for an insulating cuprate with edge-sharing chains Li2CuO2.The Hamiltonian contains the nearest and next-nearest neighboring intrachain and zigzag-type interchain interactions.The values of the interactions are obtained from the analysis of the magnetic susceptibility, and this system is found to be described as coupled frustrated chains.We calculate the dynamical spin correlation function S(q,\omega) by using the exact diagonalization method, and show that the spectra of S(q,\omega) are characterized by the zigzag-type interchain interactions. The results of the recent inelastic neutron scattering experiment are discussed in the light of the calculated spectra.

Dynamic spin-correlation function near the antiferromagnetic quantum phase transition of heavy fermions

The dynamical spin susceptibility is studied in the magnetically disordered phase of heavy-Fermion systems near the antiferromagnetic quantum phase transition. In the framework of the $S=1/2$ Kondo lattice model, we introduce a perturbative expansion treating the spin and Kondo-like degrees of freedom on an equal footing. The dynamical spin susceptibility displays a two-component behavior in agreement with the inelastic neutron scattering (INS) experiments performed in ${\mathrm{CeCu}}_{6},{\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2},$ and ${\mathrm{UPt}}_{3}:$ a quasielastic q-independent peak as in a Fermi-liquid theory, and a strongly q-dependent inelastic peak typical of a non-Fermi-liquid behavior. Very strikingly, the position of the inelastic peak is found to be pushed to zero at the antiferromagnetic transition. The picture is consistent with the neutron cross sections observed in INS experiments.

Spin Excitations and Momentum Distribution in the Two-Dimensional Extendedt-JModel

The t ′ and t ′′ -dependences of the dynamical spin correlation function S ( q , ω) of the 2D t - t ′ - t ′′ - J model are studied numerically based on the Lanczos algorithm for two holes on 4 ×4 sites. In particular the spin excitations at q =( π, π) ≡ q 0 are examined in detail and compared with results of the mean-field theory. The spin excitations turned out to be drastically different between YBCO( t ′ =-0.17, t ′′ =0.2) and YBCO(II)( t ′ =-0.5, t ′′ =0)-type, although both types reproduce the similar Fermi surfaces of YBCO and have the similar S ( q 0 , ω) in the mean-field theory. Further understanding of the properties of spin excitation for these two choices of t ′ and t ′′ are pursued by calculating the momentum distribution in the excited states. The spin excitations S ( q 0 , ω) for YBCO(II)-type are shown to be of collective type, while those for YBCO appear to be mainly individual.

Numerical evidence for SO(5) symmetry and superspin multiplets in the t– J model

In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in high-temperature superconductors. Using exact cluster diagonalization, we verify that the low-energy states of the t– J model, a widely used microscopic model for high T c cuperates, form SO(5) symmetry multiplets. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations. The dominant low-energy resonance in the dynamic spin correlation function corresponds to a 'π resonance' in the entire low doping region. The SO(5) symmetry is robust against the inclusion of longer- range Coulomb repulsion and next-nearest-neighbor hopping.

π excitation of thet−Jmodel

In this paper, we present analytical and numerical calculations of the \ensuremath{\pi} resonance in the $t\ensuremath{-}J$ model. We show in detail how the $\ensuremath{\pi}$ resonance in the particle-particle channel couples to the dynamical spin correlation function in a superconducting state. The contribution of the \ensuremath{\pi} resonance to the spin excitation spectrum can be estimated from general model-independent sum rules, and it agrees with our detailed calculations. The results are in overall agreement with the exact diagonalization studies of the $t\ensuremath{-}J$ model. Earlier calculations predicted the correct doping dependence of the neutron resonance peak in the ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ superconductor, and in this paper detailed energy and momentum dependence of the spin correlation function is presented. The microscopic equations of motion obtained within current formalism agree with that of the SO(5) nonlinear \ensuremath{\sigma} model, where the \ensuremath{\pi} resonance is interpreted as a pseudo-Goldstone mode of the spontaneous SO(5) symmetry breaking.