Antiferromagnetic Case Research Articles

Quantum phase diagram of the frustrated spin ladder with next-nearest-neighbor interactions

Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J2 = 0 is carefully analyzed.

Quantum Griffiths singularities in ferromagnetic metals

We present a theory of the quantum Griffiths phases associated with the ferromagnetic quantum phase transition in disordered metals. For Ising spin symmetry, we study the dynamics of a single rare region within the variational instanton approach. For Heisenberg symmetry, the dynamics of the rare region is studied using a renormalization group approach. In both cases, the rare region dynamics is even slower than in the usual quantum Griffiths case because the order parameter conservation of an itinerant ferromagnet hampers the relaxation of large magnetic clusters. The resulting quantum Griffiths singularities in ferromagnetic metals are stronger than power laws. For example, the low-energy density of states $\ensuremath{\rho}(\ensuremath{\epsilon})$ takes the asymptotic form $\mathrm{exp}[{{\ensuremath{-}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\lambda}}\mathrm{log}({\ensuremath{\epsilon}}_{0}/\ensuremath{\epsilon})}}^{3/5}]/\ensuremath{\epsilon}$ with $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\lambda}}$ being nonuniversal. We contrast these results with the antiferromagnetic case in which the systems show power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We also compare our result with existing experimental data of ferromagnetic alloy ${\mathrm{Ni}}_{x}{\mathrm{V}}_{1\ensuremath{-}x}$.

Finite temperature phase diagram of spin-1/2 bosons in two-dimensional optical lattice

We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations and focus on finite temperature effects. We show in two different cases, ferro- and antiferromagnetic spin-spin interactions, that the phase diagram is composed of solid Mott phases, liquid phases and superfluid phases. In the antiferromagnetic case, the superfluid (SF) is polarized while the Mott insulator (MI) and normal Bose liquid (NBL) phases are not. On the other hand, in the ferromagnetic case, none of the phases is polarized. The superfluid-liquid transition is of the Berezinsky-Kosterlitz-Thouless type whereas the solid-liquid passage is a crossover.

Counterflow instability and turbulence in a spin-1 spinor Bose-Einstein condensate

We theoretically study counterflow instability and turbulence in a spin-1 spinor Bose-Einstein condensate by the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. Our study considers (i) the dynamics induced by the counterflow of two components with different magnetic quantum numbers, which leads to turbulence with spin degrees of freedom, and (ii) the properties of the turbulence. For (i), the behavior of the condensate induced by the counterflow strongly depends on whether the spin-dependent interaction is ferromagnetic or antiferromagnetic, leading to different behaviors for the dispersion relation and the spin density vector, etc. For (ii), we numerically calculate the spectrum of the spin-dependent interaction energy, which also depends on the spin-dependent interaction. The spectrum of the spin-dependent interaction energy in the ferromagnetic case clearly exhibits a $\ensuremath{-}7/3$ power law, which can be explained by scaling analysis. The spectrum in the antiferromagnetic case seems to show some power law too, but the power exponent cannot be estimated as definitely as the ferromagnetic case.

Lifetime of magnetic excitations in supported ferromagnetic and antiferromagnetic spin-12Heisenberg chains

The lifetime of magnetic excitations in finite 1D-supported Heisenberg chains of magnetic atoms is studied theoretically for a model system formed of $S$ $=$ \textonehalf{} spins. Both ferromagnetic and antiferromagnetic cases are considered as well as open chains and rings of atoms. Different chain lengths are considered allowing extrapolation to infinite chains. All the excited magnetic states in the finite chains and rings are studied, not only the spin-wave mode. The magnetic excitations decay by electron-hole pair creation in the substrate. As the main result, for all the systems considered, the decay rate appears to vary approximately proportionally to the excitation energy of the state, with a proportionality constant independent of the strength of the Heisenberg exchange term. In certain finite systems, a stable state is evidenced at low energy, associated with a special spin coupling structure.

Effect of Spin-Orbit Interaction and Input State on Quantum Discord and Teleportation of Two-Qubit Heisenberg Systems

We study the quantum discord and teleportation of a two-qubit Heisenberg XXX chain with spin-orbit interaction. The analytical expressions of quantum discord, output state quantum discord and fidelity are obtained for this model. The classical correlation, quantum correlation and entanglement of this system depending on coupling interaction, spin-orbit interaction and temperature are investigated in detail. It is found that the quantum discord exists for the ferromagnetic case, but entanglement is zero under the same condition. We can obtain fidelity better than any classical communication protocol for the antiferromagnetic case. The robustness of quantum discord against the temperature is helpful for the realization of quantum computation.

Thermal entanglement of mixed spin XY systems

In this article, we investigate thermal entanglements of the two-site, three-site and four-site mixed spin (1/2,1) XYsystems. The entanglement versus temperature and external magnetic field is discussed. It is found that the entanglements decrease monotonically as temperature increases in the presence and absence of a weak external magnetic field. For the two-site and four-site XY systems, thermal entanglements disappear at the same temperature which is called critical temperature no matter in the ferromagnetic case or antiferromagnetic. It also shows that the critical temperature is independent of external magnetic field. For the three-site system, the corresponding critical temperature is also irrelevant to external magnetic field, while the critical temperature for the ferromagnetic case is higher than that for the antiferromagnetic case. The entanglement of XY systems can develop a few stable platform in an environment of low temperature, but the entanglement vanishes when external magnetic field exceeds some critical value. In this article, we also analyze the difference in thermal entanglement between mixed-spin system and single-spin system, and find that there exists multi-level level crossing in the mixed-spin system.

Measurement-induced disturbance and nonequilibrium thermal entanglement in a qutrit—qubit mixed spin XXZ model

We investigate the dynamics of nonequilibrium thermal quantum correlation of a qutrit-qubit mixed spin system coupled to two bosonic reservoirs at different temperatures using measurement-induced disturbance. The effects of initial states of the spins and temperatures of the reservoirs on measurement-induced disturbance and entanglement are discussed. The results demonstrate that measurement-induced disturbance is more robust than entanglement against the influence of both these factors and there is no sudden death phenomenon for measurement-induced disturbance. The dependences of steady-state measurement-induced disturbance and entanglement on coupling constant and anisotropy parameter are also studied. Steady-state entanglement vanishes for a ferromagnetic qutrit-qubit model, while steady-state measurement-induced disturbance exists for both the antiferromagnetic and ferromagnetic cases. Appropriately modulating the coupling constant and anisotropy parameter can strengthen quantum correlation.

Numerical exact diagonalization study of triangulated kagome Heisenberg spin system

The thermodynamic properties and the magnetization under magnetic field at zero temperature of the spin-1/2 Heisenberg model on triangulated kagome lattice, which composed of two sublattices, are investigated by numerical exact diagonalization method for 18 and up to 27 spin clusters, respectively. The temperature dependence of magnetic susceptibility may be reproduced qualitatively with the weak ferromagnetic intersublattice nearest neighbor exchange coupling constant JAB as proposed by previous studies, although it is quantitatively insufficient in comparison with the experimental result. The magnetization under magnetic field shows the 5/9 plateau for every examined values of JAB, but 1/3 plateau, visible in the experiment, may be reproduced only for not so weak antiferromagnetic case of JAB. This discrepancy for JAB in those two qualities has also been recognized in previous studies on classical spin models and is not still resolved even for the present quantum spin system.

Thermal Entanglement in Lipkin—Meshkov—Glick Model

We investigate the thermal entanglement in the Lipkin—Meshkov—Glick (LMG) model which consists of spin-1/2 particles with XXZ-type exchange interactions between any pair of them. The ferromagnetic (FM) and antiferromagnetic (AFM) cases are completely analyzed at both finite temperature and zero temperature. According to the results obtained by accurate numerical calculation, several interesting physic phenomena and characteristics of thermal entanglement in the LMG model are found. Not only do we evaluate the entanglement of the LMG model, but also discover the correlations between macroscopic physical quantities and thermal entanglement.

Quantum discord in the ground and thermal states of spin clusters

Quantum discord (QD) is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer which describe a number of known molecular magnets and compute the QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases, and discontinuous jumps in the magnitude of the QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD and the pairwise entanglement at T = 0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as t → ∞. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.

Thermal Entanglement in a Two-Qutrit Spin-1 Anisotropic Heisenberg Model

The negativity (N) as a measure of thermal entanglement (TE) is studied for a two-qutrit spin-1 anisotropic Heisenberg XXZ chain with Dzyaloshinskii—Moriya (DM) interaction in an inhomogeneous magnetic field in detail. The effects of the DM interaction parameter Dz on the thermal variation of the N for given values of the external magnetic field B, a parameter b which controls the inhomogeneity of B and the bilinear interaction parameters Jx = Jy ≠ Jz are obtained. It is found that N persists to higher values and to higher temperatures for the higher values of ±Dz and for the higher positive values of Jz, i.e. in the antiferromagnetic (AFM) case. When Jz < 0, the ferromagnetic (FM) case, and Dz is small, and if Jz is strong enough to compete with Dz, N decreases. In addition, N declines with the increasing values of B and b.

Excitation of spin waves by tunneling electrons in ferromagnetic and antiferromagnetic spin-12Heisenberg chains

Excitation of finite chains of magnetic atoms adsorbed on a surface by tunneling electrons from a scanning tunneling microscope tip is studied using a Heisenberg Hamiltonian description of the magnetic couplings along the chain and a strong coupling approach to inelastic tunneling. The excitation probability of the magnetic levels is very high and the excitation spectra in chains of different lengths are very similar. The excitations in finite chains can be considered as spin waves quantized in the finite object. The energy and momentum spectra of the spin waves excited in the idealized infinite chain by tunneling electrons are determined from the results on the finite chains. Both ferromagnetic and antiferromagnetic couplings are considered, leading to very different results. In particular, in the antiferromagnetic case, excitations linked to the entanglement of the chain ground state are evidenced.

KAGOME APPROXIMATION FOR 3He ON HUSIMI LATTICE WITH TWO- AND THREE-SITE EXCHANGE INTERACTIONS

The Ising approximation of the Heisenberg model in a strong magnetic field, with two-, and three-spin exchange interactions are studied on a Husimi lattice. This model can be considered as an approximation of the third layer of 3 He absorbed on the surface of graphite (kagome lattice). Using dynamic approach, we have found exact recursion relation for the partition function. For different values of exchange parameters and temperature, the diagrams of magnetization are plotted and showed that magnetization properties of the model vary from ferromagnetic to antiferromagnetic depending on the value of model parameters. For antiferromagnetic case magnetization plateau at 1/3 of saturation field is obtained. Lyapunov exponent for recursion relation are considered and showed absence of bifurcation points in thermodynamic limit. The Yang–Lee zeros are analyzed in terms of neutral fixed points and showed that Yang–Lee zeros of the model are located on the arcs of the circle with the radius R = 1.

Ground states of trapped spin-1 condensates in magnetic field

We consider a spin-1 Bose-Einstein condensate trapped in a harmonic potential under the influence of a homogeneous magnetic field. We investigate spatial and spin structure of the mean-field ground states under constraints on the number of atoms and the total magnetization. We show that the trapping potential can make the antiferromagnetic condensate separate into three distinct phases and ferromagnetic condensate into two distinct phases. In the ferromagnetic case, the magnetization is located in the center of the harmonic trap, while in the antiferromagnetic case magnetized phases appear in the outer regions. We describe how the transition from the Thomas-Fermi regime to the single-mode approximation regime with decreasing number of atoms results in the disappearance of the domains. We suggest that the ground states can be created in experiment by adiabatically changing the magnetic-field strength.

Thermal entanglement in molecular spin rings

The thermal entanglement in the triangular molecular spin ring with Dzyaloshinskii—Moriya interaction is studied. The concurrences of arbitrary two spins of the triangular molecular spin ring for various cases are evaluated. The tendency of the concurrence with Dzyaloshinskii—Moriya interaction and temperature is analysed and discussed. We note that the concurrence arrives at its maximum in the regime with the large Dzyaloshinskii—Moriya interaction and low temperature, and gradually decreases to zero with the increase of temperature. The concurrence has different features for the ferromagnetic and antiferromagnetic cases. For completeness, we also numerically calculate the concurrence of spin rings with N > 3 spins and analyse their behaviours.

Memory and aging effects in antiferromagnetic nanoparticles

We investigate slow dynamics of collection of a few noninteracting antiferromagnetic NiO nanoparticles. Our purpose is to enquire the role of size-dependent magnetization fluctuations in temperature and time dependent properties of antiferromagnetic nanoparticles. The zero-field cooled magnetization exhibits size dependent fluctuations. We find memory effects in field cooled magnetization, as well as aging effects in thermoremenant magnetization of antiferromagnetic nanoparticles. The antiferromagnetic nanoparticles show a stronger memory effect than the corresponding effect in the ferromagnetic particles, when the distribution of particles include very small sizes. The situation reverses for bigger sizes. The relaxation of the magnetization after a sudden cooling, heating and removal of fields reiterate the memory effects. We also see a weak signature of size-dependent magnetization fluctuations in aging effect of antiferromagnetic nanoparticles. We find a two-step relaxation of thermoremenant magnetization in antiferromagnetic case, which differs qualitatively from relaxation of ferromagnetic nanoparticles.

THE EFFECT OF DIFFERENT DZYALOSHINSKII–MORIYA INTERACTIONS ON TELEPORTATION VIA A TWO-QUBIT HEISENBERG CHAIN

Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J &gt; 0 (antiferromagnetic) case, which is contrary to coupling coefficient J &lt; 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J &gt; 0 case and ferromagnetic J &lt; 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J &gt; 0 case. But for J &lt; 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.

Microscopic model versus systematic low-energy effective field theory for a doped quantum ferromagnet

We consider a microscopic model for a doped quantum ferromagnet as a test case for the systematic low-energy effective field theory for magnons and holes, which is constructed in complete analogy to the case of quantum antiferromagnets. In contrast to antiferromagnets, for which the effective field theory approach can be tested only numerically, in the ferromagnetic case, both the microscopic and the effective theory can be solved analytically. In this way, the low-energy parameters of the effective theory are determined exactly by matching to the underlying microscopic model. The low-energy behavior at half-filling as well as in the single- and two-hole sectors is described exactly by the systematic low-energy effective field theory. In particular, for weakly bound two-hole states the effective field theory even works beyond perturbation theory. This lends strong support to the quantitative success of the systematic low-energy effective field theory method not only in the ferromagnetic but also in the physically most interesting antiferromagnetic case.

Critical entropy of quantum Heisenberg magnets on simple-cubic lattices

We analyze the temperature dependence of the entropy of the spin-1/2 Heisenberg model on the three-dimensional simple-cubic lattice, for both the case of antiferromagnetic and ferromagnetic nearest neighbor exchange interactions. Using optimized extended ensemble quantum Monte Carlo simulations, we extract the entropy at the critical temperature for magnetic order from a finite-size scaling analysis. For the antiferromagnetic case, the critical entropy density equals 0.341(5)$k_B$, whereas for the ferromagnet, a larger value of 0.401(5) $k_B$ is obtained. We compare our simulation results to estimates put forward recently in studies assessing means of realizing the antiferromagnetic N\'eel state in ultra-cold fermion gases in optical lattices.