The ferromagnetically coupled classical Heisenberg chain in an applied magnetic field has been studied by computer simulation. The results indicate the presence of a second collective mode, in addition to the damped spin-wave-like modes which have previously been observed in the absence of a magnetic field. For intermediate wavelengths, the mode manifests itself by well-defined oscillations in the energy-density correlation function, and by a second peak in the spectrum of the longitudinal spin-density correlation functions.
A theoretical study of the low-temperature dynamics of the antiferromagnetic Heisenberg chain in an external field is presented. The time- and frequency-dependent transverse and longitudinal spin fluctuations and energy fluctuations are calculated by means of a continued fraction representation. The frequency moments are evaluated analytically by a computer program. The transfer-operator technique is used to calculate all static correlation functions. For modest magnetic fields, a two-peak structure in the dynamic form factor of the transverse spin fluctuations is observed. Apart from the usual spin-wave excitations, the longitudinal-spin-fluctuation spectra show a broad second resonance for some temperatures and fields. The energy fluctuations display a dominant oscillatory time dependence.
A comprehensive comparison between the magnetic field- and temperature-dependent low-frequency spin dynamics in the antiferromagnetic spin-1/2 Heisenberg chain system copper pyrazine dinitrate, probed via the
13C nuclear magnetic resonance relaxation rate ${T}_{1}^{\ensuremath{-}1}$, and the field theoretical approach in the Luttinger liquid regime was performed. We found very good agreement between experiment and theory in the investigated temperature and field range. Our results demonstrate how spin-spin interactions strongly affect the spin dynamics of Heisenberg spin chain compounds in the vicinity of the quantum critical point.
Abstract Motivated by recent experimental progress on the quasi-one-dimensional quantum magnet NiNb2O6, we study the spin dynamics of an S = 1 ferromagnetic Heisenberg chain with single-ion anisotropy by using a semiclassical molecular dynamics approach. This system undergoes a quantum phase transition from a ferromagnetic to a paramagnetic state under a transverse magnetic field, and the magnetic response reflecting this transition is well described by our semiclassical method. We show that at low temperature the transverse component of the dynamical structure factor depicts clearly the magnon dispersion, and the longitudinal component exhibits two continua associated with single- and two-magnon excitations, respectively. These spin excitation spectra show interesting temperature dependence as effects of magnon interactions. Our findings shed light on the experimental detection of spin excitations in a large class of quasi-one-dimensional magnets.
The large-scale dynamics of quantum integrable systems is often dominated by ballistic modes due to the existence of stable quasiparticles. We here consider as an archetypical example for such a system the spin-
21 XXX Heisenberg chain that features magnons and their bound states. An interesting question, which we here investigate numerically, arises with respect to the fate of ballistic modes at finite temperatures in the limit of zero magnetization
m=0. At a finite magnetization density
m, the spin-autocorrelation function $\mathrm{\ensuremath{\Pi}}(x,t)$ (at high temperatures) typically exhibits a trimodal behavior with left- and right-moving quasiparticle modes and a broad center peak with slower dynamics. The broadening of the fastest propagating modes exhibits a subdiffusive
t1/3 scaling at large magnetization densities $m\ensuremath{\rightarrow}\frac{1}{2}$, familiar from noninteracting models; it crosses over into a diffusive scaling
t1/2 upon decreasing the magnetization to smaller values. The behavior of the center peak appears to exhibit a crossover from transient superdiffusion to ballistic relaxation at long times. In the limit $m\ensuremath{\rightarrow}0$, the weight carried by the propagating peaks tends to zero; the residual dynamics is carried only by the central peak; it is sub-ballistic and characterized by a dynamical exponent
z close to the value
23 familiar from Kardar-Parisi-Zhang (KPZ) scaling. We confirm that, employing elaborate finite-time extrapolations, that the spatial scaling of the correlator $\mathrm{\ensuremath{\Pi}}$ is in excellent agreement with KPZ-type behavior and analyze the corresponding corrections.