Spin Autocorrelation Research Articles

Microscopic understanding of NMR signals by dynamic mean-field theory for spins

A recently developed dynamic mean-field theory for disordered spins (spinDMFT) is shown to capture the spin dynamics of nuclear spins very well. The key quantities are the spin autocorrelations. In order to compute the free induction decay (FID), pair correlations are needed in addition. They can be computed on spin clusters of moderate size which are coupled to the dynamic mean fields determined in a first step by spinDMFT. We dub this versatile approach non-local spinDMFT (nl-spinDMFT). It is a particular asset of nl-spinDMFT that one knows from where the contributions to the FID stem. We illustrate the strengths of nl-spinDMFT in comparison to experimental data for CaF2. Furthermore, spinDMFT provides the dynamic mean fields explaining the FID of the nuclear spins of 13C in adamantane up to some static noise. The spin Hahn echo in adamantane is free from effects of static noise and agrees excellently with the spinDMFT results without further fitting.

Spin-resolved counting statistics as a sensitive probe of spin correlation in transport through a quantum dot spin valve

We investigate the noise in spin transport through a single quantum dot (QD) tunnel coupled to ferromagnetic (FM) electrodes with noncollinear magnetizations. Based on a spin-resolved quantum master equation, auto- and cross-correlations of spin-resolved currents are analyzed to reveal the underlying spin transport dynamics and characteristics for various polarizations. We find the currents of majority and minority spins could be strongly autocorrelated despite uncorrelated charge transfer. The interplay between tunnel coupling and the Coulomb interaction gives rise to an exchange magnetic field, leading to the precession of the accumulated spin in the QD. It strongly suppresses the bunching of spin tunneling events and results in a unique double-peak structure in the noise of the net spin current. The spin autocorrelation is found to be susceptible to magnetization alignments, which may serve as a sensitive tool to measure the magnetization directions between the FM electrodes.

Spin dynamics of quantum Ising chain in random correlated magnetic fields

The spin dynamics of one-dimensional quantum Ising chain with random correlated magnetic fields (RCMFs) is studied at the high-temperature limit by the recursion method. Both the spin autocorrelation function and its corresponding spectral density are investigated under the circumstance of bimodal-type and Gaussian-type RCMFs. It is found that the dynamics of the system are highly dependent on the correlated mode and strength between the longitudinal and transverse magnetic fields (i.e., Bxi and Bzi). Due to the cooperation or synergy effect between Bxi and Bzi, crossovers between different dynamical behaviors can be revealed in most of the cases. In general, the dynamics of the system is dominant by the field (Bxi or Bzi) with a larger proportion when the RCMFs are weak. However, when the RCMFs are strong, the system tends to exhibit a disordered behavior, which manifests as a multiple-peak feature in the bimodal-type case or a broaden spectral in the Gaussian-type case. In another perspective, when the proportion of Bzi is small, the central-peak behavior can be enhanced by increasing the proportion of Bxi. Interestingly, when the proportion of Bzi is large, the perturbation of Bxi on Bzi tends to excite new dynamical behavior. Our results indicate that using RCMF to manipulate the spin dynamics of the Ising system may be a new try.

The BKT transition and its dynamics in a spin fluid.

We study the effect of particle mobility on phase transitions in a spin fluid in two dimensions. The presence of a phase transition of the BKT universality class is shown in an off-lattice model of particles with purely repulsive interaction employing computer simulations. A critical spin wave region 0 < T < TBKT is found with a nonuniversal exponent η(T) that follows the shape suggested by BKT theory, including a critical value consistent with ηBKT = 1/4. One can observe a transition from power-law decay to exponential decay in the static correlation functions at the transition temperature TBKT, which is supported by finite-size scaling analysis. A critical temperature TBKT = 0.17(1) is suggested. Investigations into the dynamic aspects of the phase transition are carried out. The short-time behavior of the incoherent spin autocorrelation function agrees with the Nelson-Fisher prediction, whereas the long-time behavior differs from the finite-size scaling known for the static XY model. Analysis of coherent spin wave dynamics shows that the spin wave peak is a propagating mode that can be reasonably well fitted by hydrodynamic theory. The mobility of the particles strongly enhances damping of the spin waves, but the model still lies within the dynamic universality class of the standard XY model.

Effects of autocorrelated disorder on the dynamics in the vicinity of the many-body localization transition

The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of autocorrelated disorder on the static and dynamical properties of a one-dimensional many-body quantum system which exhibits many-body localization. Specifically, by means of some standard measures of energy level repulsion and localization of energy eigenstates, we show that a strong degree of correlations between the on-site potentials in the one-dimensional spin-1/2 Heisenberg model leads to suppression of the many-body localization phase, while level repulsion is mitigated for small disorder strengths, although energy eigenstates remain well extended. Our findings are also remarkably manifested in the time domain, on which we put the main emphasis, as shown by the time evolution of experimentally relevant observables, like the return probability and the spin autocorrelation function.

Role of quantum fluctuation ininducing ergodicity inthe spin glass phase and its effect inquantum annealing.

We review the numerical studies on the critical behaviour of the quantum Sherrington-Kirkpatrick (SK) spin glass model, which indicate that aquantum critical behaviour is observed up to a low but non-zero value of temperature. We revisit the numerical investigations on the spin glass order parameter distributions, which identify a low temperature along with high transverse field spin glass phase where the order parameter distribution becomes a delta function in the thermodynamic limit indicating the restoration of replica symmetry and ergodic nature of the system. In the remaining spin glass phase associated with high temperature and low transverse field, the observed distribution is broad akin to the Parisi order parameter distribution. This essentially indicates the non-ergodic behaviour of the system. We further discuss the annealing dynamics studies on the quantum SK model. Such investigations reveal the system size independence of annealing time when the annealing paths go through the ergodic spin glass region. Interestingly, when such dynamics are performed in the non-ergodic spin glass phase the annealing time becomes an increasing function of the system size. Spin autocorrelation shows faster relaxation in the ergodic spin glass region compared with that found in the non-ergodic spin glass region. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Nuclear-spin polaron formation: Anisotropy effects and quantum phase transition

We study theoretically the formation of the nuclear-spin polaron state in semiconductor nanosystems within the Lindblad equation approach. To this end, we derive a general Lindblad equation for the density operator that complies with the symmetry of the system Hamiltonian and address the nuclear-spin polaron formation for localized charge carriers subject to an arbitrarily anisotropic hyperfine interaction when optically cooling the nuclei. The steady-state solution of the density matrix for an anisotropic central spin model is presented as a function of the electron and nuclear spin bath temperature. Results for the electron-nuclear spin correlator as well as data for the nuclear spin distribution function serve as a measure of spin-entanglement. The features in both of them clearly indicate the formation of the nuclear polaron state at low temperatures where the crossover regime coincides with an enhancement of quantum fluctuations and agrees with the mean-field prediction of the critical temperature line. We can identify two distinct polaron states dependent upon the hyperfine anisotropy which are separated by a quantum phase transition at the isotropic point. These states are reflected in the temporal spin auto-correlation functions accessible in experiment via spin-noise measurements.

Thermodynamics of the classical spin triangle

Abstract The classical spin system consisting of three spins with Heisenberg interaction is an example of a completely integrable mechanical system. In this paper, we explicitly calculate thermodynamic quantities such as density of states, specific heat, susceptibility and spin autocorrelation functions. These calculations are performed (semi-)analytically and shown to agree with corresponding Monte Carlo simulations. It is shown that the thermodynamic functions depend qualitatively on the character of the system in terms of its frustration, especially w. r. t. their low temperature limit. For the long-time autocorrelation function, we find, for certain values of the coupling constants, a decay to constant values in the form of an 1/t damped harmonic oscillation and propose a theoretical explanation.

Dynamic mean-field theory for dense spin systems at infinite temperature

A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S=\frac{1}{2}$ and external field. For large coordination numbers, it is shown that the effect of the environment of each spin is captured by a classical time-dependent random mean field which is normally distributed. Expectation values are calculated by averaging over these mean fields, i.e., by a path integral over the normal distributions. A self-consistency condition is derived by linking the moments defining the normal distributions to spin autocorrelations. In this framework, we explicitly show how the rotating-wave approximation becomes a valid description for increasing magnetic field. We also demonstrate that the approach can easily be extended. Exemplarily, we employ it to reach a quantitative understanding of a dense ensemble of spins with dipolar interaction which are distributed randomly on a plane including static Gaussian noise as well.

Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems

We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite temperature spin autocorrelation function decays at long times as $t^{-\beta}$ with $\beta < 0.5$, indicating subdiffusive transport at strong disorders.

Integer quantum Hall effect of the α−T3 model with a broken flat band

Despite the intense amount of attention and huge potential of two-dimensional (2D) magnets for applications in novel magnetic, magneto-optical, magneto-thermal and magneto-electronic devices, there has yet to be a robust strategy developed to systematically understand magnon-magnon (MMI) interactions at finite temperature. In this paper, we present a first-principles theoretical method to introduce the finite temperature magnon-magnon interaction into Heisenberg Hamiltonian through a nonlinear correction energy. The Wick theorem is used to decouple the four-magnon operators to two-magnon order. We demonstrate the capabilities of this method by studying the strength of MMI in Cr2Ge2Te6 (CGT) monolayer. The spin wave spectrum at finite temperature and the time-dependent spin autocorrelation function are explored. It is found that the magnon relaxation time due to magnon-magnon scattering increases with temperature because of the reduction in magnon energy, while decreases with wavevector and external magnetic field. Our results provide a new insight to understand the magnon damping and energy dissipation in two-dimensional ferromagnetic materials.

Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems

Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, R\'enyi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.

High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging Kardar-Parisi-Zhang scaling in the zero-magnetization limit

The large-scale dynamics of quantum integrable systems is often dominated by ballistic modes due to the existence of stable quasi-particles. We here consider as an archetypical example for such a system the spin-$\frac{1}{2}$ XXX Heisenberg chain that features magnons and their bound states. An interesting question, which we here investigate numerically, arises with respect to the fate of ballistic modes at finite temperatures in the limit of zero magnetization $m{=}0$. At a finite magnetization density $m$, the spin autocorrelation function $\Pi(x,t)$ (at high temperatures) typically exhibits a trimodal behavior with left- and right-moving quasi-particle modes and a broad center peak with slower dynamics. The broadening of the fastest propagating modes exhibits a sub-diffusive $t^{1/3}$ scaling at large magnetization densities, $m {\rightarrow} \frac{1}{2}$, familiar from non-interacting models; it crosses over into a diffusive scaling $t^{1/2}$ upon decreasing the magnetization to smaller values. The behavior of the center peak appears to exhibit a crossover from transient super-diffusion to ballistic relaxation at long times. In the limit $m{\to}0$, the weight carried by the propagating peaks tends to zero; the residual dynamics is carried only by the central peak; it is sub-ballistic and characterized by a dynamical exponent $z$ close to the value $\frac{3}{2}$ familiar from Kardar-Parisi-Zhang (KPZ) scaling. We confirm, employing elaborate finite-time extrapolations, that the spatial scaling of the correlator $\Pi$ is in excellent agreement with KPZ-type behavior and analyze the corresponding corrections.

Open XXZ chain and boundary modes at zero temperature

We study the open XXZ spin chain in the anti-ferromagnetic regime and for generic longitudinal magnetic fields at the two boundaries. We discuss the ground state via the Bethe ansatz and we show that, for a chain of even length L and in a regime where both boundary magnetic fields are equal and bounded by a critical field, the spectrum is gapped and the ground state is doubly degenerate up to exponentially small corrections in L. We connect this degeneracy to the presence of a boundary root, namely an excitation localized at one of the two boundaries. We compute the local magnetization at the left edge of the chain and we show that, due to the existence of a boundary root, this depends also on the value of the field at the opposite edge, even in the half-infinite chain limit. Moreover we give an exact expression for the large time limit of the spin autocorrelation at the boundary, which we explicitly compute in terms of the form factor between the two quasi-degenerate ground states. This, as we show, turns out to be equal to the contribution of the boundary root to the local magnetization. We finally discuss the case of chains of odd length.

Thouless and relaxation time scales in many-body quantum systems

A major open question in studies of nonequilibrium quantum dynamics is the identification of the time scales involved in the relaxation process of isolated quantum systems that have many interacting particles. We demonstrate that long time scales can be analytically found by analyzing dynamical manifestations of spectral correlations. Using this approach, we show that the Thouless time, $t_{\text{Th}}$, and the relaxation time, $t_{\text{R}}$, increase exponentially with system size. We define $t_{\text{Th}}$ as the time at which the spread of the initial state in the many-body Hilbert space is complete and verify that it agrees with the inverse of the Thouless energy. $t_{\text{Th}}$ marks the point beyond which the dynamics acquire universal features, while relaxation happens later when the evolution reaches a stationary state. In chaotic systems, $t_{\text{Th}}\ll t_{\text{R}}$, while for systems approaching a many-body localized phase, $t_{\text{Th}}\rightarrow t_{\text{R}}$. Our analytical results for $t_{\text{Th}}$ and $t_{\text{R}}$ are obtained for the survival probability, which is a global quantity. We show numerically that the same time scales appear also in the evolution of the spin autocorrelation function, which is an experimental local observable. Our studies are carried out for realistic many-body quantum models. The results are compared with those for random matrices.

Unveiling spin-glass transition and antiferromagnetic order by μSR studies in spin-chain Sm2BaNiO5

We report the zero-field and longitudinal field muon spin relaxation studies in a spin-chain compound Sm2BaNiO5. Two magnetic transitions, that have not been previously detected by the heat capacity and magnetization measurements, are confirmed at 46 and 9 K. The antiferromagnetic order is suggested at 46 K. Analysis of the muon spin polarization unveils the spin-glass transition at 9 K. Time-field scaling relation of the muon spin polarization verifies the spin–spin autocorrelation function following the cut-off power law, which is approximated by the Ogielski form, as employed numerically for characterizing the spin-glasses.

Nonuniversal critical aging scaling in three-dimensional Heisenberg antiferromagnets

We numerically investigate the stationary and non-equilibrium critical dynamics in three-dimensional isotropic Heisenberg antiferromagnets. Since the non-conserved staggered magnetization couples dynamically to the conserved magnetization density, we employ a hybrid simulation algorithm that combines reversible spin precession with relaxational Kawasaki spin exchange processes. We measure the dynamic critical exponent and identify a suitable intermediate time window to obtain the aging scaling exponents. Our results support an earlier renormalization group prediction: While the critical aging collapse exponent assumes a universal value, the associated temporal decay exponent in the two-time spin autocorrelation function depends on the initial distribution of the conserved fields; here, specifically on the width of the initial spin orientation distribution.

On the Effect of an Inhomogeneous Magnetic Field on High-Frequency Asymptotic Behaviors of Correlation Functions of Spin Lattices

Singular points of spin autocorrelation functions on the imaginary time axis, which determine the arguments of exponential high-frequency asymptotic behaviors, have been analyzed. It has been shown that randomly distributed inhomogeneous magnetic fields expand the wings of spectra of autocorrelation functions and, thereby, intensify the heating of a system subjected to variable magnetic fields, which are used to create effective Hamiltonians or at the saturation of inhomogeneously broadened EPR lines.

Superaging and Subaging Phenomena in a Nonequilibrium Critical Behavior of the Structurally Disordered Two-Dimensional XY Model

A Monte Carlo numerical simulation of the specific features of nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a low-temperature initial state. On the basis of the analysis of the two-time dependence of autocorrelation functions and dynamic susceptibility for systems with spin concentrations of p = 1.0, 0.9, and 0.6, aging phenomena characterized by a slowing down of the relaxation system with increasing waiting time and the violation of the fluctuation–dissipation theorem (FDT) are revealed. The values of the universal limiting fluctuation–dissipation ratio (FDR) are obtained for the systems considered. As a result of the analysis of the two-time scaling dependence for spin–spin and connected spin autocorrelation functions, it is found that structural defects lead to subaging phenomena in the behavior of the spin–spin autocorrelation function and superaging phenomena in the behavior of the connected spin autocorrelation function.

Spin dynamics of random Ising chain in coexisting transverse and longitudinal magnetic fields

The dynamics of the random Ising spin chain in coexisting transverse and longitudinal magnetic fields is studied by the recursion method. Both the spin autocorrelation function and its spectral density are investigated by numerical calculations. It is found that system’s dynamical behaviors depend on the deviation σJ of the random exchange coupling between nearest-neighbor spins and the ratio rlt of the longitudinal and the transverse fields: (i) For rlt=0, the system undergoes two crossovers from N independent spins precessing about the transverse magnetic field to a collective-mode behavior, and then to a central-peak behavior as σJ increases. (ii) For rlt≠0, the system may exhibit a coexistence behavior of a collective-mode one and a central-peak one. When σJ is small (or large enough), system undergoes a crossover from a coexistence behavior (or a disordered behavior) to a central-peak behavior as rlt increases. (iii) Increasing σJ depresses effects of both the transverse and the longitudinal magnetic fields. (iv) Quantum random Ising chain in coexisting magnetic fields may exhibit under-damping and critical-damping characteristics simultaneously. These results indicate that changing the external magnetic fields may control and manipulate the dynamics of the random Ising chain.