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Journal of Physics Conference Series

Interaction of solitons with a qubit in an anisotropic Heisenberg spin chain with first and second-neighbor interactions

S. K. Varbev, Iavor I. Boradjiev, R S Kamburova, Hassan Chamati

Published Feb 1, 2021• 1 citation
Publisher

Abstract

Abstract Solitons provide a promising means to control the state of a spin-qubit in quantum information technology. In this paper, we consider the anisotropic interaction between a soliton, propagating in a ferromagnetic Heisenberg spin chain and a spin- <?CDATA $\frac{1}{2}$?> 1 2 particle (qubit). The spin chain exhibits an on-site anisotropy and spin-spin nearest-neighbor and next-nearest-neighbor interactions. The Bloch sphere picture is employed to investigate the spin- <?CDATA $\frac{1}{2}$?> 1 2 dynamics. We found that increasing the anisotropic and the second neighbor interactions leads to an increase of the deviation of the spin- <?CDATA $\frac{1}{2}$?> 1 2 particle from its initial state.

DOI
10.1088/1742-6596/1762/1/012018

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Abstract Solitons provide a promising means to control the state of a spin-qubit in quantum information technology. In this paper, we consider the anisotropic interaction between a soliton, propagating in a ferromagnetic Heisenberg spin chain and a spin- <?CDATA $\frac{1}{2}$?> 1 2 particle (qubit). The spin chain exhibits an on-site anisotropy and spin-spin nearest-neighbor and next-nearest-neighbor interactions. The Bloch sphere picture is employed to investigate the spin- <?CDATA $\frac{1}{2}$?> 1 2 dynamics. We found that increasing the anisotropic and the second neighbor interactions leads to an increase of the deviation of the spin- <?CDATA $\frac{1}{2}$?> 1 2 particle from its initial state.
The interaction between solitons, propagating in a magnetic chain, with a qubit is studied. The spin chain is described by the Heisenberg model in a nearest-neighbour approximation with anisotropy. The quantum bit (qubit) is modeled by a two level quantum system. The equation for the evolution of the qubit is obtained. The role of the parameters of the soliton for the quantum bit dynamics is investigated. The results are analyzed using a geometrical representation for the qubit as a Bloch sphere.
Abstract The dynamical behavior of the quantum state of different quantum spin chains, with designed site-dependent interaction strengths, is analyzed when the initial state belongs to the one excitation subspace. Our results show that the inhomogeneous chains transfer single excitations with near-perfect fidelity for two different spin chain Hamiltonians. The first one is the ferromagnetic Heisenberg Hamiltonian with nearest neighbor interactions. The second spin chain has long-range anisotropic interactions, ferromagnetic in one direction and antiferromagnetic in the orthogonal plane. Both designed chains have in common a partially ordered spectrum and well-localized eigenvectors. This physical trait unifies the description of both kinds of systems.
The excitation spectrum is studied around the degenerate point at the Ising limit in the one-dimensional anisotropic Heisenberg antiferromagnets with next-nearest-neighbor interactions. Solitons are found as propagation modes in the N\'eel state and in the (2,2) antiphase state, while triplet-dimer excitations are found propagating in the dimer state. These excitations determine the shape of dynamical spin-correlation functions, which are calculated by an exact diagonalization for finite chains. The phase diagram is determined from the condition that the energy gap vanishes in the excitation spectrum.
The phenomenon of quantum entanglement has a very important role in quantum mechanics. Particularly, the quantum spin chain provides a platform for theoretical and experimental investigation of many-body entanglement. In this paper, we investigate time evolution of entanglement in a four-qubit anisotropic Heisenberg XXZ chain with nearest neighboring (NN), the next nearest neighboring (NNN), and the Dzialoshinskii-Moriya (DM) interactions. Calculations of the entanglement evolution of the Werner state carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, frustration, etc. The results show that for the Werner state, DM interaction and the frustration parameters play important roles. Furthermore, results show that the time evolution of the Werner state entanglement may be useful to capture the quantum phase transitions in quantum magnetic systems.
Elementary excitations are studied near the Ising limit close to the degenerate point in the one-dimensional anisotropic Heisenberg antiferromagnets with up to next-nearest-neighbor interactions. Solitons in the Néel and (2,2) antiphase states and triplet-dimer excitations in the dimer state are found as propagating modes. These excitations are found to dominate the shape of the central peak in dynamical spin correlation functions, through the comparison with the numerical results by an exact diagonalization method for finite chains. The temperature dependence of the static correlation function is also discussed, and the shape is found to change gradually with increasing temperature, approaching the zero-temperature correlation function at the degenerate point.