Narrow Results

We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi–Dirac functions. To accommodate the spin density matrix, the distribution functions become 2 × 2 matrix-valued. From an analytic perspective, the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The numerical scheme could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.

Using Suzuki–Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special cases, also conserve the energy and maintain time reversibility. We investigate integration schemes of up to eighth order and show that these new algorithms can be used with much larger time steps than a well established predictor–corrector method. These methods may lead to a substantial speedup of spin dynamics simulations, however, the choice of which order method to use is not always straightforward.

We consider model A dynamics for a quench from the disordered into the ordered phase of SU(3) lattice gauge theory and the analogue 3d 3-state Potts model. For the gauge model this corresponds to a rapid heating from the confined to the deconfined phase. The exponential growth factors of low-lying structure function modes are numerically calculated. The linear theory of spinodal decomposition is used to determine the critical modes. This allows for the Debye screening mass estimation in an effective phenomeno-logical model. The quench leads to competing vacuum domains, which make the equilibration of the QCD vacuum after the heating non-trivial. The influence of such domains on the gluonic energy density is studied.

A generalization of the Yang–Lee and Fisher zeros on far-from-equilibrium systems coupled with two thermal baths is proposed. The Yang–Lee zeros were obtained for minimal models which exhibit complicated behavior in the context of the partition function zeros and provide an analitycal treatment. This type of model may be considered as a simplest one and analogous to Ising model for equilibrium. The obtained distributions of generalized Yang–Lee zeros show nontrivial behavior for these simple models.

Monogamy of entanglement is a quantum mechanical property that limits quantum correlations shared among many parties. In an example strongly interacting spin system we examine approaches for approximating the ground state energy both from above and below by mean-field and N-representability methods, respectively. Due to strong competition among the terms in the Hamiltonian, the resulting ground-state wavefunction, although is entangled, does not possess entanglement that is proportional to the system size, thus obeying the monogamy of entanglement.

Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends on the inability of the system to recover the phases. Gaussian decaying in time of the fidelity is proved for spin systems and radiation-matter interaction.

We present analytic expressions for the temperature dependent magnetization and magnon dispersion relation of the antiferromagnetic (AFM) EuTe. This bulk semiconductor represent a concentrated spin system for which the interaction between magnons has to be taken into account. We do this using the renormalized spin wave theory. A higher order Green's function according to Tjablikov is used for their description. As a result, we obtain a modified Bloch-T^3/2 law, for low temperatures and high magnetic fields. A full analytic expression is given for the sublattice magnetization of the AFM EuTe (B₀ = 0), with a Néel temperature of T_N = 9.81 K. In the case of EuTe, the magnon excitation energies exhibit a characteristic maximum. For q = 0, an energy gap E_g occurs in the spin wave spectrum, a consequence of the AFM exchange interaction J₂(T). Such energy gaps exist in the spectrum of magnon excitation energies only in systems with AFM interactions.

We study by means of the Landau–Lifshitz equation both the dynamical and the thermodynamical equilibrium properties of the interacting anisotropic magnetic particles on a chain in the presence of an applied magnetic field. The interaction between the magnetic particles is produced by an exchange coupling between first neighbors with periodic boundary conditions. We find that the total magnetization modulus can be a fluctuating function of time, since the system under study contains anisotropic terms. We obtain an analytical expression for the configurational temperature and an approximate formula for the case of a large number of particles. When the direction of the external field is different to the easy axes, the configurational temperature presents an oscillatory behavior as a function of time. Finally, by using the time average of the temperature, we calculate both the energy and the magnetization along the external field as a function of temperature, recovering the equilibrium thermodynamics results.

If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not efficiently simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical "questions" more efficiently. The existence of one-to-one mappings between different algebras of observables or between different Hilbert spaces allow us to represent and imitate any physical system by any other one (e.g. a bosonic system by a spin-1/2 system). We explain how these mappings can be performed, and we show quantum networks useful for the efficient evaluation of some physical properties, such as correlation functions and energy spectra.

We introduce a general scheme to realize perfect quantum state reconstruction and storage in systems of interacting qubits. This novel approach is based on the idea of controlling the residual interactions by suitable external controls that, acting on the inter-qubit couplings, yield time-periodic inversions in the dynamical evolution, thus cancelling exactly the effects of quantum state diffusion. We illustrate the method for spin systems on closed rings with XY residual interactions, showing that it enables the massive storage of arbitrarily large numbers of local states, and we demonstrate its robustness against several realistic sources of noise and imperfections.

The correlations between a pair of spins in a many-spin state encoded in the diagonal and off-diagonal spin–spin correlation functions. These spin functions determine the quantum correlation measures, like pair-wise concurrence, quantum discord and other measures of quantum information. We show that for isotropic and translationally invariant states, the quantum correlations depend only on the diagonal spin correlation function. The pair concurrence shows a strict short-ranged behavior. The distribution of concurrence for a random W-like state exhibits a long tail for both time-reversal invariant states and for states that break the time reversal. The quantum discord can be related to the diagonal spin correlation function. As the spin function is long range close to a critical point, analogously the quantum discord exhibits a long range behavior. For the isotropic state, the conditional entropy distribution is a Dirac delta function, whereas it has a twin-peak structure for the anisotropic model.

A spin-star system consisting of three peripheral two-state systems and a central one is considered, with the peripheral spins assumed to interact with each other, as well as with the central one. It is shown that such two couplings, each one being a thermal entanglement source, can significantly compete in the formation of quantum correlations in the thermal state to the point that they can destroy any thermal entanglement of the peripheral spins.

In this paper, we study integrable multilayer spin systems, namely, the multilayer M-LIII equation. We investigate their relation with the geometric flows of interacting curves and surfaces in some space $R^n$. Then we present their Lakshmanan equivalent counterparts. We show that these equivalent counterparts are, in fact, the vector nonlinear Schrödinger equation (NLSE). It is well known that the vector NLSE is equivalent to the $\mathrm{\Gamma }$-spin system. Also, we have presented the transformations which give the relation between solutions of the $\mathrm{\Gamma }$-spin system and the multilayer M-LIII equation. It is interesting to note that the integrable multilayer M-LIII equation contains constant magnetic field $H$. It seems that this constant magnetic vector plays an important role in the theory of “integrable multilayer spin system” and in nonlinear dynamics of magnetic systems. Finally, we present some classes of integrable models of interacting vortices.

Monogamy of entanglement is a quantum mechanical property that limits quantum correlations shared among many parties. In an example strongly interacting spin system we examine approaches for approximating the ground state energy both from above and below by mean-field and N-representability methods, respectively. Due to strong competition among the terms in the Hamiltonian, the resulting ground-state wavefunction, although is entangled, does not possess entanglement that is proportional to the system size, thus obeying the monogamy of entanglement.