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Physical review. B./Physical review. B

Staggered field induced dynamical effects in a quantum spin chain

Andrei A. Zvyagin

Published Jun 21, 2018• 5 citations
Publisher

Abstract

The response of the one-dimensional antiferromagnetic spin-1/2 chain to the ac staggered magnetic field is studied within the Hartree-Fock-like approximation. For a closed system that field produces oscillations of the magnetization with the frequency of the ac field, modulated by the large number of small Rabi frequencies. In the open system the Rabi oscillations decay due to relaxation processes. It is shown that those oscillations also contribute to the dynamics of the entanglement of the system. The calculated temperature and frequency dependence of the dynamical characteristics is strictly nonmonotonic, reflecting the complicated character of the common action of the homogeneous and staggered dc field.

DOI
10.1103/physrevb.97.214425

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The response of the one-dimensional antiferromagnetic spin-1/2 chain to the ac staggered magnetic field is studied within the Hartree-Fock-like approximation. For a closed system that field produces oscillations of the magnetization with the frequency of the ac field, modulated by the large number of small Rabi frequencies. In the open system the Rabi oscillations decay due to relaxation processes. It is shown that those oscillations also contribute to the dynamics of the entanglement of the system. The calculated temperature and frequency dependence of the dynamical characteristics is strictly nonmonotonic, reflecting the complicated character of the common action of the homogeneous and staggered dc field.
With the help of the exact solution of the Kitaev model the parametric pumping of the two-dimensional quantum spin liquid under the action of the ac magnetic field is studied. In the dynamical regime the field produces oscillations of the magnetization with the field's frequency, modulated by the Rabi-like oscillations. In the steady-state regime, the Rabi-like oscillations are damped. The absorption of the ac field by the Kitaev spin model is finite and manifests resonance features. Such a behavior is generic for quantum spin liquids with fermionic excitations, and it is different from the linear spin-wave response of magnetically ordered systems to such a parametric pumping.
Using the density-matrix-renormalization-group technique, we calculate numerically the low-energy excitation spectrum and magnetization curve of the spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected to describe the physics of the ${R}_{2}{\mathrm{BaNiO}}_{5} (R\ensuremath{\ne}Y)$ family below the N\'eel temperature of the magnetic rare-earth (R) sublattice. These results are valid in the entire range of the staggered field, and agree with those given by the nonlinear $\ensuremath{\sigma}$ model study for small fields, but differ from the latter for large fields. They are consistent with the available experimental data. The correlation functions for this model are also calculated. The transverse correlations display the anticipated exponential decay with shorter correlation length, while the longitudinal correlations show explicitly the induced staggered magnetization.
The quantum entanglement dynamics of a one-dimensional spin-1/21/21/2 anisotropic XXZ\mathit{XXZ}XXZ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.
The response of an open spin chain with isotropic antiferromagnetic interactions to a uniform magnetic field is studied by classical Monte Carlo simulations. It is observed how the induced on-site magnetization is nonuniform, due to the occurrence of edge staggered terms which decay exponentially over a distance equal to the zero-field correlation length of the infinite chain. The total magnetic moment associated to each staggered term is found to be about half of the original single-spin magnitude and to decrease as the inverse of temperature (i.e., to behave as a Curie-like moment). The numerical results are compared to recent NMR findings in spinless-doped Y2BaNiO5;{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5};Y2​BaNiO5​; the remarkable agreement found shows that, for temperatures above the Haldane gap, the classical approach gives a correct picture of the boundary effects observed in the Heisenberg S=1S=1S=1 chain.
The effect of the circularly polarized laser field on quantum spin systems in the steady-state regime, in which relaxation plays the central role, has been studied. The dynamical mean-field-like theory predicts several general results for the behavior of the time-average magnetization caused by the laser field. The induced magnetization oscillates with the frequency of the laser field (while Rabi-like oscillations, which modulate the latter in the dynamical regime, are damped by the relaxation in the steady-state regime). At high frequencies, that magnetization is determined by the value to which the relaxation process is directed. At low frequencies the slope of that magnetization as a function of the frequency is determined by the strength of the laser field. The anisotropy determines the resonance behavior of the time-averaged magnetization in both the ferromagnetic and antiferromagnetic cases with nonzero magnetic anisotropy. Nonlinear effects (in the magnitude of the laser field) have been considered. The effect of the laser field on quantum spin systems is maximal in resonance, where the time-averaged magnetization, caused by the laser field, is changed essentially. Out of resonance the changes in the magnetization are relatively small. The resonance effect is caused by the nonzero magnetic anisotropy. The resonance frequency is small (proportional to the anisotropy value) for spin systems with ferromagnetic interactions and enhanced by exchange interactions in the spin systems with antiferromagnetic couplings. We show that it is worthwhile to study the laser-field-induced magnetization of quantum spin systems caused by the high-frequency laser field in the steady-state regime in ``easy-axis'' antiferromagnetic spin systems (e.g., in Ising-like antiferromagnetic spin-chain materials). The effects of the Dzyaloshinskii-Moriya interaction and the spin-frustration couplings (in the case of the zigzag spin chain) have been analyzed.
Static and dynamical properties of weakly coupled antiferromagnetic spin chains are treated using a mean-field approximation for the interchain coupling and exact results for the resulting effective one-dimensional problem. Results for staggered magnetization, N\'eel temperature, and spin wave excitations are in agreement with experiments on KCuF3{\mathrm{KCuF}}_{3}KCuF3​. The existence of a narrow longitudinal mode is predicted. The results are in agreement with general scaling arguments, contrary to spin wave theory.