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Journal of Physics Condensed Matter

Relaxation of kinks in the Ising chain with a transverse field interacting with a three-dimensional phonon field

Jasmina Tekić, Zoran M. Ivić, S. Stamenković, R. B. Žakula

Published Jan 6, 1992• 2 citations
Publisher

Abstract

The influence of phonon fluctuations on the dynamics of kink-like domain-wall excitations in the one-dimensional Ising model with a transverse field (s=1/2) was investigated. It was found that such non-linear excitations behave almost like classical Brownian particles. This is the consequence of the emission and absorption of acoustic phonons excited by domain walls propagating through the vibrating lattice. The effective friction and diffusion constants are also evaluated. It was established that the overall process has the character of Cherenkov-type radiation.

DOI
10.1088/0953-8984/4/1/033

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The influence of phonon fluctuations on the dynamics of kink-like domain-wall excitations in the one-dimensional Ising model with a transverse field (s=1/2) was investigated. It was found that such non-linear excitations behave almost like classical Brownian particles. This is the consequence of the emission and absorption of acoustic phonons excited by domain walls propagating through the vibrating lattice. The effective friction and diffusion constants are also evaluated. It was established that the overall process has the character of Cherenkov-type radiation.
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We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for the discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We show that the domain wall spectrum shows a band structure consisting of 2S2S2S nonintersecting zones.
We study effects of a transverse magnetic field on the properties of the one-dimensional spin-1/2 Ising-like antiferromagnet. In order to emphasize the relevant role of domain walls between opposite antiferromagnetic domains, the spin Hamiltonian is exactly mapped to the interacting fermion Hamiltonian, via the dual transformation as well as the Jordan-Wigner transformation. Within the generalized Hartree-Fock approximation, we find that the excitation spectrum exhibits characteristic features, which are explained as a result of the different roles of the transverse field and of the transverse components of the exchange interactions in the propagation of the domain wall. At a critical field where the excitation gap vanishes, a ground-state phase transition is found to take place in the same manner as that in the transverse Ising model. In addition, we discuss the relevance of our magnetization curve with regard to experimental data in CsCoCl 3 .
We study the decoherence dynamics of a quantum Ising lattice of finite size with a transverse dissipative interaction, namely, the coupling with the bath is assumed perpendicular to the direction of the spins interaction and parallel to the external magnetic field. In the limit of small transverse field, the eigenstates and spectrum are obtained by a strong-coupling expansion, from which we derive the Lindblad equation in the Markovian limit. At temperature lower than the energy gap and for weak dissipation, the decoherence dynamics can be restricted to take only the two degenerate ground states and the first excited subspace into account. The latter is formed by pairs of topological excitations (domain walls or kinks), which are quantum delocalized along the chain due to the small magnetic field. We find that some of these excited states form a relaxation-free subspace, namely, they do not decay to the ground states.