Time-dependent Spin Correlation Functions Research Articles

High-temperature dynamics in quantum compass models

We analyze the high temperature spin dynamics of compass models using a moment expansion. We point out that the evaluation of moments maps to the enumeration of paths in a branching process on the lattice. This mapping to a statistical mechanics combinatorics problem provides an elegant visualization of the analysis. We present results for the time dependent spin correlation function (which is of relevance to NMR experiments) for two compass models: the Kitaev honeycomb model and two-dimensional compass model.

Density of states of one-dimensional Pauli ionic conductor

Microscopic one-dimensional noninteracting model for the description of the energy spectrum of the ion subsystem in ionic conductor is considered. The processes of ionic hoppings are described in terms of Pauli operators. Time-dependent correlation functions hb(t)b + (0)ij in Pauli operators are obtained using the exact numerical procedure known for time-dependent spin correlation functions. The frequency dependence of autocorrelation function Jbb+(!) is calculated and analysed at the wide range of temperatures. The frequency and temperature dependences of the one-particle density of states are investigated.

Quantum entanglement dynamics and decoherence wave in spin chains at finite temperatures

We analyze the quantum entanglement at the equilibrium in a class of exactly solvable one-dimensional spin models at finite temperatures and identify a region where the quantum fluctuations determine the behavior of the system. We probe the response of the system in this region by studying the spin dynamics after projective measurement of one local spin which leads to the appearance of the ``decoherence wave.'' We investigate time-dependent spin correlation functions, the entanglement dynamics, and the fidelity of the quantum information transfer after the measurement.

Rotating-frame nuclear magnetic relaxation of spins diffusing on a disordered lattice: a Monte Carlo model

The rotating-frame nuclear magnetic relaxation rate of spins diffusing on a disordered lattice has been calculated by Monte Carlo methods. The disorder includes not only variation in the distances between neighbouring spin sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent spin correlation functions which translate into asymmetry in the characteristic peak in the temperature dependence of the dipolar relaxation rate. The results may be used to deduce the average hopping rate from the relaxation but the effect is not sufficiently marked to enable the distribution of the hopping rates to be evaluated. The distribution, which is a measure of the degree of disorder, is the more interesting feature and it has been possible to show from the calculation that measurements of the relaxation rate as a function of the strength of the radiofrequency spin-locking magnetic field can lead to an evaluation of its width. Some experimental data on an amorphous metal - hydrogen alloy are reported which demonstrate the feasibility of this novel approach to rotating-frame relaxation in disordered materials.

Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization

All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J \sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + \Delta S_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $\Delta=0 , \cos(0.3\pi)$, and 1. The dynamic spin pair correlations $< S_{l+n}^{\mu}(t) S_l^{\mu} > , (\mu=x,z)$, the dynamic structure factors $S^{\mu}(q,\omega)$, and the intermediate structure factors $I^{\mu}(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,\omega)$ is mainly concentrated on the region $|\omega| < \varepsilon_2(q)$, where $\varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^{\mu}(q,t)$ for $\Delta \neq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.

Quantum spin dynamics of the transverse Ising model in two dimensions

The authors use the method of recurrence relations to obtain the time-dependent spin correlation function of the Ising model in a transverse field in 2D. They find that the correlation function decays algebraically at long times as t{sup {minus}{alpha}}, where {alpha} {le} 2.2. This is to be contrasted with the 1D case where the decay is Gaussian. They expect that in 3D the dynamical correlation will also exhibit a power law decay. Their results can be used to understand the experimental shape functions for the induced moment in LiTb{sub p}Y{sub 1{minus}p}F{sub 4}. 10 refs., 3 figs.

Time-dependent thermodynamic properties of the Ising model from damage spreading

The relationship between damage spreading and static thermodynamic properties in the Ising model developed by Coniglioet al. is here extended to include time-dependent thermodynamic quantities. We exploit this new result to measure the time-dependent spin correlation function from damage spreading in the Ising model with heat bath and Glauber dynamics. Until now, only static thermodynamic quantities have been correctly determined from damage spreading, and even then, only with heat bath dynamics. We also show that there are significant differences between the kinetics of damage spreading as found in heat bath and Glauber dynamics.

Two-Level System Coupled to Phonons: A Discrete Path-Integral Method

A discrete path-integral representation for the partition function of a two-level tunneling system coupled to acoustic phonons is derived. This representation allows calculation of properties in the whole coupling range. As a function of the coupling there is an abrupt (ground-state) transition from the weak-coupling regime to the self-trapped state. From a moment analysis of the time-dependent spin-correlation function it follows that there is loss of phase coherence if the coupling exceeds the critical coupling. In this regime the mean effective tunneling rate vanishes linearly with temperature.

Combined three-dimensional polarization analysis and spin echo study of spin glass dynamics

We report direct measurements of the time-dependent spin correlation function S( k, t) for a Cu -Mn spin glass alloy over nearly 3 decades of time in a single scan in the range 10 -12 < t < 10 -9 s. This was achieved by using, for the first time, a combination of neutron spin echo and polarization analysis techniques. The results show most clearly the particular dynamics of spin glasses, namely a behaviour that can be described by a spectrum of relaxation times spreading over a wide range.

Correlation functions for the Heisenberg-Ising chain at T=0

The longitudinal and transverse space and time dependent spin correlation functions for the one-dimensional Heisenberg-Ising model are derived asymptotically in the weak-coupling-low-frequency-long-wavelength limit within the framework of ordinary many-body theory (field theory). By means of the Jordan-Wigner transformation and using methods developed previously for the Tomonaga model (1950), the zero-temperature correlation functions is expressed as functional integrals. The associated one-body problem is explicitly soluble in the asymptotic regions and the correlation functions assume the form of Gaussian integrals which are evaluated analytically in the weak-coupling-low-frequency-long-wavelength limit. Apart from a linear correction to the transverse exchange constant agreement with Luther and Peschel (1975) is obtained.

Transverse time-dependent spin correlation functions for the one-dimensional XY model at zero temperature

We compute exactly the transverse time-dependent spin-spin correlation functions 〈 S x 1(0) S x R+1 ( t)〉 and 〈 S y 1(0) S y R+1 ( t)〉 at zero temperature for the one-dimensional XY model that is defined by the hamiltonian H N = - Σ N i=1 [(1 + γ)S x iS x i+1 + (1 − γ)S y iS y i+1 + hS z i] . We then analyze these correlation functions in two scaling limits: (a) γ fixed, h → 1, R → ∞, t → ∞ such that ‖(h − 1)/γ‖[R 2 − γ 2t 2] 1 2 is fixed, and (b) h fixed less than one, γ → 0 +, R → ∞, t → ∞ such that γ[R 2 − (1 − h 2)t 2] 1 2 is fixed. In these scaling regions we give both a perturbation expansion representation of the various scaling functions and we express these scaling functions in terms of a certain Painlevé transcendent of the third kind. From these representations we study both the small and large scaling variable limits in both the space-like and time-like regions.

Time correlation functions and ergodic properties in the alternating XY-chain

Explicit expressions for the time-dependent spin correlation functions are derived for the one-dimensional alternating XY-model in zero field. The ergodic properties of the wave-number dependent magnetization are discussed. It is found that the magnetization is ergodic, apart from exceptional cases, such as e.g. the homogeneous XY-model.

Phenomenological description of dynamics in a diluted anisotropic heisenberg paramagnet at high temperatures

AbstractA recent work on space and time dependent spin correlation function for a diluted isotropic Heisenberg paramagnet at infinite temperature is generalized in two important directions: firstly, now also lattices are considered which, admit nearest neighbour triangles, e.g. f.c.c. lattice, and, secondly, now the exchange interaction is allowed to be uni‐axially Anisotropic. The latter generalization necessitates the consideration of two different types of spin‐correlations: longitudinal and transverse. As limiting cases, the longitudinal correlation is examined for XY model and the transverse spin correlation for the Ising model. Between these limits, correlations are computed for J0/J+ = 2 and 0.5, for several concentrations, and the results are compared with those for the isotropic case, i.e. J0/J+ = 1.

Dynamics of the Two-Dimensional Finite Heisenberg Model

Time-dependent spin-correlation functions of the two-dimensional finite (3×3=9) isotropic Heisenberg model (spin=1/2) have been calculated at infinite temperatures. The numerical results thus obtained are similar to those of the linear Heisenberg chain.

Correlation functions in Heisenberg magnetic chains: Quantum effects at low temperatures

A theoretical approach to the one-dimensional isotropic Heisenberg model at low temperatures is presented which uses rotationally invariant combinations of spin operators only and is thus adapted to treat correctly effects resulting from the absence of long-range order in these systems. Analytic expressions for space- and time-dependent spin correlation functions are given for small values of T/JS/sup 2/ and 1/S. The results include an expression for the spin correlation function in the antiferromagnetic ground state and a discussion of changes in line shape, due to quantum effects, for short-wavelength magnons as observed in neutron scattering experiments. (auth)

Time-dependent fluctuations in spin systems in d dimensions

The time-dependent spin-correlation function is investigated near T c in d dimensions, by a microscopic kinetic theory in a model with long-range forces. For the isotropic ferromagnet it is shown that there exists at least a large precritical region where, in the absence of a magnetic field and for T > T c , dynamic scaling holds up to d = 6. In the range 4 < d < 6, however, the characteristics frequency does not scale from above to below T c, since there are two distinct scaling lengths below T c. For d > 6 the results agree with the conventional (Van Hove) theory. Conjectures are made about the true critical behavior, and a detailed comparison is presented between the kinetic theory and the phenomenological theory of dynamic scaling. For the anti-ferromagnet the conventional theory is recovered for d ≥ −4

Time-dependent spin-correlation functions in anisotropic systems: I. Infinite-temperature kinetic equations in the presence of a crystal field

We present in this paper the technical tools necessary to derive kinetic equations for anisotropic spin systems with arbitrary spin; to simplify, we limit ourselves to infinite temperature and to the simplest possible crystal-field anisotropy. We also apply this technique to the derivation of explicit, but approximate, kinetic equations for the direct and indirect spin-autocorrelation functions. The solution of these equations will be discussed in another publication.

Temperature Dependence of the Linewidth in Critical Spin Fluctuation

Starting from the kinetic equations obeyed by the time-dependent spin-correlation functions, we have calculated the homogeneous function which appears in the dynamical scaling expression for the linewidth of critical fluctuations in ferromagnets and antiferromagnets. In agreement with recent experimental findings, this function shows a minimum for κq inverse correlation length/wavenumber 0. © 1970 The American Physical Society.