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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Antiferromagnetic anisotropic XXZ chain of spins S= 1/2 in the presence of an inhomogeneous transverse magnetic field as a basis for the multiqubit quantum register simulation

A. A. Kokin, V. A. Kokin

Published Dec 18, 2014• 0 citations
Publisher

Abstract

This article presents the results of studies of the linear antiferromagnetic spin chain with uniaxial anisotropy (XXZ– model) placed in a transverse magnetic field directed along the anisotropy axis of the chain with a constant gradient along the chain. A spin Hamiltonian for the states close to the ground was written in the spin-wave approximation. It was diagonalized by an asymptotic expansion in the small parameter describing the magnitude of the field gradient. Local energy of the ground state and the reduced density matrix of the quantum states for a selected pair of spins in the chain have been considered in the gapped and gapless cases. Local spin polarization and the local toroidal magnetic moment have also been found. Local pair entanglement of quantum states as a characteristic of quantum correlations in the spin chain was studied.

DOI
10.1117/12.2181023

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This article presents the results of studies of the linear antiferromagnetic spin chain with uniaxial anisotropy (XXZ– model) placed in a transverse magnetic field directed along the anisotropy axis of the chain with a constant gradient along the chain. A spin Hamiltonian for the states close to the ground was written in the spin-wave approximation. It was diagonalized by an asymptotic expansion in the small parameter describing the magnitude of the field gradient. Local energy of the ground state and the reduced density matrix of the quantum states for a selected pair of spins in the chain have been considered in the gapped and gapless cases. Local spin polarization and the local toroidal magnetic moment have also been found. Local pair entanglement of quantum states as a characteristic of quantum correlations in the spin chain was studied.
As a nuclear spin model of scalable quantum register, the one-dimensional chain of the magnetic atoms with nuclear spins 1/2 substituting the basic atoms in the plate of nuclear spin free easy-axis 3D antiferromagnet is considered. It is formulated the generalized antiferromagnet Hamiltonian in spin-wave approximation (low temperatures) considering the inhomogeneous external magnetic field, which is directed along the easy axis normally to plane of the plate and has a constant gradient along the nuclear spin chain. Assuming a weak gradient, the asymptotic expression for coefficients of unitary transformations to the diagonal form of antiferromagnet Hamiltonian is found. With this result the expression for indirect interspin coupling, which is due to hyperfine nuclear electron coupling in atoms and the virtual spin wave propagation in antiferromagnet ground state, was evaluated. It is shown that the inhomogeneous magnetic field essentially modifies the characteristics of indirect interspin coupling. The indirect interaction essentially grows and even oscillates in relation to the interspin distance when the local field value in the middle point of two considered nuclear spin is close to the critical field for quantum phase transition of spin-flop type in bulk antiferromagnet or close to antiferromagnetic resonance. Thus, the external magnetic field, its gradient, microwave frequency and power can play the role of control parameters for qubit states. Finally, the one and two qubit states decoherence and longitudinal relaxation rate are caused by the interaction of nuclear spins with virtual spin waves in antiferromagnet ground state are calculated.
We have investigated the zero-and finite-temperature behaviors of the anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of a transverse magnetic field (h). The attention is concentrated on an interval of magnetic field between the factorizing field (h(f)) and the critical one (h(c)). The model presents a spin-flop phase for 0 < h < h(f) with an energy scale which is defined by the long range antiferromagnetic order while it undergoes an entanglement phase transition at h = h(f). The entanglement estimators clearly show that the entanglement is lost exactly at h = h(f), which justifies different quantum correlations on both sides of the factorizing field. As a consequence of zero entanglement (at h = h(f)) the ground state is known exactly as a product of single-particle states which is the starting point for initiating a spin wave theory. The linear spin wave theory is implemented to obtain the specific heat and thermal entanglement of the model in the interested region. A double-peak structure is found in the specific heat around h = h(f), which manifests the existence of two energy scales in the system as a result of two competing orders before the critical point. These results are confirmed by the low temperature Lanczos data which we have computed.
We study the interplay of electric and magnetic order in the one-dimensional Heisenberg spin-12\frac{1}{2}21​ XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (DM) interaction and with longitudinal and transverse magnetic fields, interpreting the DM interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped N\'eel phase with antiferromagnetic (AF) order, gapped saturated phase, and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the N\'eel phase (even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.
We consider the determination of the ground state energy and the lowest lying excitations for ferromagnetic Heisenberg spin chains with uniaxial anisotropy of the “easy plane” type in an external magnetic field directly along the anisotropy axis. The ratio of the anisotropy and exchange constants (α) is assumed small, but the size of the site spin S is arbitrary. To first order in α the exact results are shown to differ from the quasiclassical results only by the substitution α→α˜=α[1−(1/2)S]. The asymptotic behavior of the transverse spin correlation function is discussed, and a comparison is made between the theoretical results and recent experiment data.
We study the tuning effect of a transverse magnetic field on the confinement of spinons in the infinite XXZ spin-1/2 chain. The spinon confinement in this model takes place in the gapped antiferromagnetic phase upon application of a staggered longitudinal magnetic field. The tuning transverse magnetic field has mutually orthogonal uniform and staggered components. The energy spectra of the two-spinon bound states (the ``mesons'') in the confinement regime are analytically calculated in this model using two different perturbative schemes. The first one applies in the extreme anisotropic (Ising) limit and employs the inverse anisotropy constant as a small parameter. The second perturbative scheme, which applies at any anisotropy in the gapped antiferromagnetic domain, exploits the integrability of the XXZ spin chain at zero magnetic field. The small parameters in the second technique are the components of the transverse, and staggered longitudinal magnetic fields. It is shown that the weak transverse magnetic field mixes the transverse and longitudinal meson modes, and leads to an avoided crossing of their energies upon increase of its strength. The explicit formulas for the two-spinon contribution to the dynamical structure factors of local spin operators are obtained as well in this model in the weak confinement regime for wave vectors close to the points k=0k=0k=0 and $\ensuremath{\pi}$.
By exploiting density-matrix renormalization group techniques, we investigate the spin dynamics of a spin-1/2 one-dimensional J 1 - J 2 XXZ model with competing ferromagnetic J 1 and antiferromagnetic J 2 exchange couplings under applied magnetic fields. Numerical results of spin excitation spectra show that in the field-induced spin quadrupole regime, the longitudinal component has a gapless mode and the transverse component has a gapped mode irrespective of the exchange anisotropy. The excitation gap of the transverse spin excitation increases as the exchange anisotropy increases over the XY-like and Ising-like regions, demonstrating that two-magnon bound states are stabilized due to the easy-axis anisotropy.