We present a combination of analytic calculations and a powerful numerical method for large spin baths in the low-field limit. The hyperfine interaction between the central spin and the bath is fully captured by the density matrix renormalization group. The adoption of the density matrix renormalization group for the central spin model is presented and a proper method for calculating the real-time evolution at infinite temperature is identified. In addition, we study to which extent a semiclassical model, where a quantum spin-1/2 interacts with a bath of classical Gaussian fluctuations, can capture the physics of the central spin model. The model is treated by average Hamiltonian theory and by numerical simulation.

We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S. Uhrig, Phys. Rev. B 88, 155305 (2013) by the explicit consideration of the conservation of the total spin. On the classical level, we compare the results of the classical equations of motions in absence and presence of an external field to the full quantum result obtained by density-matrix renormalization (DMRG). We show that for large bath sizes and not too low magnetic field the classical dynamics, averaged over Gaussian distributed initial spin vectors, agrees quantitatively with the quantum-mechanical one. This observation paves the way for an efficient approach for certain parameter regimes.Comment: 13 pages, 9 figure

Recent neutron scattering studies revealed the three dimensional character of the magnetism in the iron pnictides and a strong anisotropy between the exchange perpendicular and parallel to the spin stripes. We extend studies of the J1-J2-Jc Heisenberg model with S = 1 using selfconsistent spin-wave theory. A discussion of two scenarios for the instability of the columnar phase is provided. The relevance of a biquadratic exchange term between in-plane nearest neighbors is discussed. We introduce mean-field decouplings for biquadratic terms using the Dyson-Maleev and the Schwinger boson representation. Remarkably their respective mean-field theories do not lead to the same results, even at zero temperature. They are gauged in the Néel phase in comparison to exact diagonalization and series expansion. The J1-J2-Jc model is analyzed under the influence of the biquadratic exchange J bq and a detailed description of the staggered magnetization and of the magnetic excitations is given. The biquadratic exchange increases the renormalization of the in-plane exchange constants which enhances the anisotropy between the exchange parallel and perpendicular to the spin stripes. Applying the model to iron pnictides, it is possible to reproduce the spin-wave dispersion for CaFe2As2 in the direction perpendicular to the spin stripes and perpendicular to the planes. Discrepancies remain in the direction parallel to the spin stripes which can be resolved by passing from S = 1 to S = 2. In addition, results for the dynamical structure factor within the self-consistent spin-wave theory are provided.

Mazur's inequality renders statements about persistent correlations possible. We generalize it in a convenient form applicable to any set of linearly independent constants of motion. This approach is used to show rigorously that a fraction of the initial spin correlations persists indefinitely in the isotropic central spin model unless the average coupling vanishes. The central spin model describes a major mechanism of decoherence in a large class of potential realizations of quantum bits. Thus the derived results contribute significantly to the understanding of the preservation of coherence. We will show that persisting quantum correlations are not linked to the integrability of the model, but caused by a finite operator overlap with a finite set of constants of motion. PACS numbers: 78.67.Hc, 72.25.Rb, 03.65.Yz, 02.30.Ik a. Introduction. The two-time correlation function of two observables reveals important information about the dynamics of a system in and out of equilibrium: The noise spectra are obtained from symmetric combinations of correlation functions, while the causal, antisymmetric combination determines the susceptibilities required for the theory of linear response.The two-time correlation function only depends on the time difference if at t = 0 the system of interest is prepared in a stationary state whose density operator commutes with the time-independent Hamiltonian. This is what will be considered in this work. Since correlations generically decay for t → ∞, important information about the system dynamics is gained if a non-decaying fraction of correlations prevails at infinite times. Such non-decaying correlations are clearly connected to a limited dynamics in certain subspaces of the Hilbert space. The question arises if such a restricted dynamics is always linked to the integrability of the Hamiltonian. Here integrability means that the Hamiltonian can be diagonalized by Bethe ansatz which implies that there is an extensive number of constants of motion. Identifying and understanding those non-decaying correlations can be potentially exploited in applications for persistent storage of (quantum) information.In this Letter we first prove that persisting correlations are not restricted to integrable systems by using a generalized form of Mazur's inequality 1,2 . This is in contrast to the behavior of the Drude weight in the frequency-dependent conductivity of one-dimensional systems which appears to vanish abruptly once the integrability is lost, even if only by including an arbitrarily small perturbation. So far, the Drude weight has been the most common application of Mazur's inequality, see for instance Refs. 3-6 and references therein. Second, we apply this approach to the central spin model (CSM) 7 describing the interaction of a single spin, e.g., an electronic spin in a quantum dot 8,9 , an effective two-level model in a NV center in diamond 10 , or a 13 C nuclear spin 11 , coupled to a bath of surrounding nuclear spins inducing decoherence.Persisting spin correlations have been found in ...