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Journal of Physics Condensed Matter

Polaron-like features of the domain wall in a classical Ising chain with transverse field

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

Published Aug 23, 1993• 1 citation
Publisher

Abstract

The possibility of the creation of the bound state of a domain wall and surrounding lattice distortion was investigated in the framework of the one-dimensional Ising model with transverse field. It was found that the existence of such an entity is very sensitive to the mutual ratio of the basic physical parameters of the system. The authors obtain that, in the weak-coupling regime, such a 'dressed' excitation can arise in the so-called unadiabatic limit when the maximal photon energy greatly exceeds the nearest-neighbour exchange energy. In that case, the 'dressing' effect can significantly modify domain-wall properties, causing the increase of its effective mass and lowering of the ground-state energy, while the domain-wall velocity cannot exceed the speed of sound.

DOI
10.1088/0953-8984/5/34/013

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The possibility of the creation of the bound state of a domain wall and surrounding lattice distortion was investigated in the framework of the one-dimensional Ising model with transverse field. It was found that the existence of such an entity is very sensitive to the mutual ratio of the basic physical parameters of the system. The authors obtain that, in the weak-coupling regime, such a 'dressed' excitation can arise in the so-called unadiabatic limit when the maximal photon energy greatly exceeds the nearest-neighbour exchange energy. In that case, the 'dressing' effect can significantly modify domain-wall properties, causing the increase of its effective mass and lowering of the ground-state energy, while the domain-wall velocity cannot exceed the speed of sound.
We discuss several problems concerning domain walls in the spin-S Ising model at zero temeprature in a magnetic field, H/(2S), applied in the x direction. Some results are also given for the planar (y-z) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small H and numerically over a large range of H. We obtain the spin-density profile by fixing the spins at opposite ends of the chain to have opposite signs of Sz{\mathit{S}}_{\mathit{z}}Sz​. One dimensional is special in that there the quantum width of the wall is proportional to the size L of the system. We also study the quantitative features of the ``particle'' band which extends up to energies of order H above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy J/S involving creation of more walls. At large S this particle band develops energy gaps and the lowest subband has tunnel splittings of order H${2}^{1\mathrm{\ensuremath{-}}2\mathit{S}}$. This scale of of energy gives rise to anomalous scaling with respect to (a) finite size, (b) temperature, or (c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum effects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall.
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 .
Within the classical and quantum S= 1 / 2 versions of the one-dimensional Ising model in a transverse field non-linear domain-wall-like excitations are studied. For the quantum case a domain wall (DW) wavefunction is constructed from the first (improper) excitation band. Various one-DW expectation values are then calculated. In particular, it is shown that the proposed DW wavefunction indeed yields the expected stationary-wall-like profile for the (S l z ) expectation value. Results are compared with the ones obtained for the classical model and used to analyse the quantum-classical correspondence of domain walls in both models. The extension to non-stationary quantum DW is briefly discussed.
We present experimental and theoretical evidence of novel bound state formation in the low transverse field ordered phase of the quasi-one-dimensional Ising-like material CoNb2O6{\text{CoNb}}_{2}{\text{O}}_{6}CoNb2​O6​. High-resolution single-crystal inelastic neutron scattering measurements observe that small transverse fields lead to a breakup of the spectrum into three parts, each evolving very differently upon increasing field. This can be naturally understood starting from the excitations of the ordered phase of the transverse field Ising model, domain wall quasiparticles (solitons). Here, the transverse field and a staggered off-diagonal exchange create one-soliton hopping terms with opposite signs. We show that this leads to a rich spectrum and a special field, when the strengths of the off-diagonal exchange and transverse field match, at which solitons become localized; the highest field investigated is very close to this special regime. We solve this case analytically and find three two-soliton continua, along with three novel bound states. Perturbing away from this novel localized limit, we find very good qualitative agreement with the experimental data. We also present calculations using exact diagonalization of a recently refined Hamiltonian model for CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ and using diagonalization of the two-soliton subspace, both of which provide a quantitative agreement with the observed spectrum. The theoretical models qualitatively and quantitatively capture a variety of nontrivial features in the observed spectrum, providing insight into the underlying physics of bound state formation.
We consider the thermal and critical behavior of the square Ising lattice with frustrated first- and second-neighbor interactions. A low-temperature domain-wall analysis including kinks and dislocations shows that there is a close relation between this classical model and the Hamiltonian of an Ising chain in a transverse field provided that the ratio of the next-nearest--to--nearest-neighbor coupling is close to 1/2. Due to the field-inversion symmetry of the Ising-chain Hamiltonian, the thermal properties of the classical system are symmetrical with respect to this coupling ratio. In the neighborhood of this regime critical exponents of the model turn out to belong to the Ising universality class. Our results are compared with previous Monte Carlo simulations.
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.