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Journal of Applied Physics

Domain-wall excitations in the spin-(1)/(2) X X Z linear chain: A new variational approach

G. Gómez-Santos

Published May 1, 1990• 0 citations
Publisher

Abstract

The linear chain XXZ spin- (1)/(2) Hamiltonian is mapped onto a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The domain-wall Hamiltonian is solved within the simplest Hartree–Fock approximation with results in very good agreement with the exact solution in the antiferromagnetic regime. The location of ordered and disordered (critical) phases is correct and low-lying excitations are well described and easily interpreted in terms of domain walls. Our domain-wall version of the original Hamiltonian is shown to provide the natural framework for a physical understanding of this system in the antiferromagnetic regime.

DOI
10.1063/1.345898

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The linear chain XXZ spin- (1)/(2) Hamiltonian is mapped onto a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The domain-wall Hamiltonian is solved within the simplest Hartree–Fock approximation with results in very good agreement with the exact solution in the antiferromagnetic regime. The location of ordered and disordered (critical) phases is correct and low-lying excitations are well described and easily interpreted in terms of domain walls. Our domain-wall version of the original Hamiltonian is shown to provide the natural framework for a physical understanding of this system in the antiferromagnetic regime.
The XXZ spin-1/2 Hamiltonian in the linear chain is exactly transformed into a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The ground state of the new Hamiltonian is studied with the Hartree-Fock approximation. This approximation is shown to become exact in the XY and extreme antiferromagnetic limits, with excellent results in between. Known results concerning the existence or nonexistence of long-range order and gap in the excitation spectrum are reproduced by our solution. Good quantitative agreement with representative properties of the exact solution is obtained. The domain-wall Hamiltonian is shown to be the natural framework for the understanding of the ground state and low-lying excited states of the XXZ system in the antiferromagnetic regime.
A physically motivated approach is used to study the linear chain XXZ spin-1 Hamiltonian in the antiferromagnetic regime. A variational Hamiltonian is obtained restricting the basis set to states with local antiferromagnetic environments separated by sites with Sz=0 acting as domain walls. Ground-state properties of this variational Hamiltonian are obtained and, in particular, an order–disorder transition is found with critical behavior corresponding to the two-dimensional Ising model universality class, in agreement with Haldane conjecture. Excellent agreement with finite chain data concerning the position of Haldane’s point, ground-state energy, and elementary excitations is found.
The XXZ spin-1 chain is studied by means of a physically motivated variational approach. An effective Hamiltonian for the dynamics of spin-0 defects in antiferromagnetic environments (domain walls) is obtained, and its ground-state properties are analyzed. An order-disorder transition is found with critical behavior corresponding to the 2D Ising model universality class, in complete agreement with Haldane conjecture. The approximations involved in this variational scheme are carefully tested using known Monte Carlo results. In particular, excellent agreement with the recently calculated excited states at the Heisenberg (isotropic) point is found, clarifying the nature of these excitations.
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 .
A variational calculation yields an eigenstate representing a domain wall-type solution for various quantum-mechanical spin models. Heisenberg Hamiltonians with local and exchange anisotropy, and an Ising model in a transverse field (including its critical regime) are discussed in detail. The domain walls are viewed as localized solutions of non-linear equations. The extent to which the results for the transverse field Ising model may be mapped on to a currently interesting “double well” anhurmonic lattice problem are analysed.