Nearest-neighbor Correlation Function Research Articles

Effects of dust particle number on the structure and dynamics in a binary complex plasma system by Langevin dynamics simulation

In this paper, Langevin dynamics simulation is used to study the influence of particle number on the structures and dynamics of a binary complex plasma, in which two kinds of particles with different masses are considered. The structures of the binary system are characterized by particle distribution, nearest-neighbor, and pair correlation function. The dynamics of the system are characterized by the evolution of average speed and kinetic energy as time, the mean square displacement (MSD) and self-diffusion coefficient of the binary particles. The lattice structures and the dynamics evolution of binary particles versus the particle number are investigated in detail in this paper. The space distribution shows that the binary particles easily fully separate themselves for a small particle number. The dynamics evolutions indicate that small particles reach the system center first, and then are pushed out by the later reached large particles. As the number of particles increases, the system becomes more ordered and the kinetic energy difference between the two kinds of particles becomes smaller. This study shows that the structure and dynamics of a binary complex plasma can be affected by dust particle number.

Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model

We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.

Inferring interactions of time-delayed dynamic networks by random state variable resetting

Time delays exist widely in real systems, and time-delayed interactions can result in abundant dynamic behaviors and functions in dynamic networks. Inferring the time delays and interactions is challenging due to systematic nonlinearity, noises, a lack of information, and so on. Recently, Shi et al. proposed a random state variable resetting method to detect the interactions in a continuous-time dynamic network. By arbitrarily resetting the state variable of a driving node, the equivalent coupling functions of the driving node to any response node in the network can be reconstructed. In this paper, we introduce this method in time-delayed dynamic networks. To infer actual time delays, the nearest neighbor correlation (NNC) function for a given time delay is defined. The significant increments of NNC originate from the delayed effect. Based on the increments, the time delays can be reconstructed and the reconstruction errors depend on the sampling time interval. After time delays are accurately identified, the equivalent coupling functions can also be reconstructed. The numerical results have fully verified the validity of the theoretical analysis.

The 2D non self-dual Ising lattices: An exact renormalization group treatment

In this work, an exact renormalization group treatment of honeycomb lattice leading to an exact relation between the coupling strengths of the honeycomb and the triangular lattices is presented. Using the honeycomb and the triangular duality relation, the critical coupling values of honeycomb and triangular lattices are calculated exactly by the simultaneous solution of the renormalized relation and the duality relation, without using the so-called star-triangular transformation. Apparently, the obtained coupling relation is unique. It not only takes place the role of the star triangular relation, but it is also the only exact relation obtained from renormalization group theory other than the 1D Ising chain. An exact pair correlation function expression relating the nearest neighbors and the next nearest neighbor correlation functions are also obtained for the honeycomb lattice. Utilizing this correlation relation, an exact expression of the correlation length of the honeycomb lattice is calculated analytically for the coupling constant values less than the critical value in the realm of the scaling theory. The critical exponents [Formula: see text] and [Formula: see text] are also calculated as [Formula: see text] and [Formula: see text].

Blue-noise sampling for human retinal cone spatial distribution modeling

This paper proposes a novel method for modeling retinal cone distribution in humans. It is based on Blue-noise sampling algorithms being strongly related with the mosaic sampling performed by cone photoreceptors in the human retina. Here we present the method together with a series of examples of various real retinal patches. The same samples have also been created with alternative algorithms and compared with plots of the center of the inner segments of cone photoreceptors from imaged retinas. Results are evaluated with different distance measure used in the field, like nearest-neighbor analysis and pair correlation function. The proposed method can effectively describe features of a human retinal cone distribution by allowing to create samples similar to the available data. For this reason, we believe that the proposed algorithm may be a promising solution when modeling local patches of retina.

Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations

We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.

Effective model with strong Kitaev interactions for α−RuCl3

We use an exact numerical diagonalization method to calculate the dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet $\alpha$-RuCl$_3$. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor (NN) spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the $\Gamma$ point in the DSFs increases with increasing NN spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering (INS) experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the NN spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both INS experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in $\alpha$-RuCl$_3$ is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between NN pairs, rather than by the strong Kitaev interactions.

Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model

Using determinant quantum Monte Carlo (DQMC) simulations, we systematically study the doping dependence of the crossover from one to two dimensions and its impact on the magnetic properties of the Hubbard model. A square lattice of chains is used, in which the dimensionality can be tuned by varying the interchain coupling $t_\perp$. The dynamical spin structure factor and static quantities, such as the static spin susceptibility and nearest-neighbor spin correlation function, are characterized in the one- and two-dimensional limits as a benchmark. When the dimensionality is tuned between these limits, the magnetic properties, while evolving smoothly from one to two dimensions, drastically change regardless of the doping level. This suggests that the spin excitations in the two-dimensional Hubbard model, even in the heavily doped case, cannot be explained using the spinon picture known from one dimension. The DQMC calculations are complemented by cluster perturbation theory studies to form a more complete picture of how the crossover occurs as a function of doping and how doped holes impact magnetic order.

Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables.

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.

Correlation Effects on Charge Order and Zero-Gap State in the Organic Conductor α-(BEDT-TTF)2I3

The effects of electron correlation in the quasi-two-dimensional organic conductor \alpha-(BEDT-TTF)2I3 are investigated theoretically by using an extended Hubbard model with on-site and nearest-neighbor Coulomb interactions. A variational Monte Carlo method is applied to study its ground-state properties. We show that there appears a nonmagnetic horizontal-stripe charge order in which nearest-neighbor correlation functions indicate a tendency toward a spin-singlet formation on the bonds with large transfer integrals along the charge-rich stripe. Under uniaxial pressure, a first-order transition from the nonmagnetic charge order to a zero-gap state occurs. Our results on a spin correlation length in the charge-ordered state suggest that a spin gap is almost unaffected by the uniaxial pressure in spite of the suppression of the charge disproportionation. The relevance of these contrasting behaviors in spin and charge degrees of freedom to recent experimental observations is discussed.

COM(3p) Solution of the 2D Hubbard Model: Momentum-Resolved Quantities

Recently, within the framework of the Composite Operator Method, it has been proposed a three-pole solution for the two-dimensional Hubbard model [Eur. Phys. J. B 87, 45 (2014)], which is still considered one of the best candidate model to microscopically describe high-$T_{c}$ cuprate superconductors. The operatorial basis comprise the two Hubbard operators (complete fermionic local basis) and the electronic operator dressed by the nearest-neighbor spin fluctuations. The effectiveness of the approximate solution has been proved through a positive comparison with different numerical methods for various quantities. In this article, after recollecting the main analytical expressions defining the solution and the behavior of basic local quantities (double occupancy and chemical potential) and of the quasi-particle energy dispersions, we resolve and analyze the momentum components of relevant quantities: filling (i.e. the momentum distribution function), double occupancy and nearest-neighbor spin correlation function. The analysis is extended to COM(2p) solutions that will be used as primary reference. Thanks to this, the role played by the third field, with respect to the two Hubbard ones, in determining the behavior of many relevant quantities and in allowing the extremely good comparison with numerical results is better understood giving a guideline to further improve and, possibly, optimize the application of the COM to the Hubbard model.

Néel temperature and thermodynamics of the half-filled three-dimensional Hubbard model by diagrammatic determinant Monte Carlo

We study the thermodynamics of the three-dimensional Hubbard model at half filling on approach to the N\'eel transition by means of large-scale unbiased diagrammatic determinant Monte Carlo simulations. We obtain the transition temperature in the strongly correlated regime, as well as the temperature dependence of the energy, entropy, double occupancy, and nearest-neighbor spin correlation function. Our results improve the accuracy of previous unbiased studies and present accurate benchmarks in the ongoing effort to realize the antiferromagnetic state of matter with ultracold atoms in optical lattices.

Schmidt gap and quantum phase transitions in the XXZ model under external field on the Bethe lattice

Along the line developed in a recent paper by one of the authors (Li W., von Delft J. and Xiang T., Phys. Rev. B, 86 (2012) 195137), a simple update scheme, as an optimal method for optimizing the infinite tree tensor network (iTTN) states, is utilized to study the XXZ model under external field on the Bethe lattice. The ground-state energy, bipartite entanglement, order parameters, and nearest-neighbor correlation functions are calculated in the framework of the iTTN states. With increasing external field, two quantum phase transitions (QPTs) (a first-order and a second-order one) take place successively. Between the antiferromagnetic phase and the saturated ferromagnetic phase, there exists another intermediate (canted Néel) phase, in which both x-axis antiferromagnetic order and unsaturated z-axis ferromagnetic order coexist. An interesting spin-flop transition between antiferromagnetic phase and canted Néel phase is observed. The model-independent bipartite entanglement is found to be capable of describing all the QPTs. It is interesting that the Schmidt gap acts as a local order parameter, and can also be used to describe the QPTs.

Matrix product state and quantum phase transitions in the one-dimensional extended quantum compass model

The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of QCM ground states, and are numerically determined by imaginary time projections. The ground state energy, correlations, quantum entanglement and its spectrum, local and nonlocal order parameters, etc., are calculated and studied in details. It is revealed that the bipartite and block entanglement entropies, as well as the nearest neighbor correlation functions can be used to detect the second-order QPTs, but not the first-order ones, while fidelity detections can recognize both. The entanglement spectrum is extracted from the MPS wavefunction, and found to be doubly degenerate in disordered phases of QCM, where non-local string order parameters exist. Moreover, with linearized tensor renormalization group method, the specific heat curves are evaluated and their low temperature behaviors are investigated.

A DEEP 1.2 mm MAP OF THE LOCKMAN HOLE NORTH FIELD

We present deep 1.2 mm continuum mapping of a 566 arcmin^2 area within the Lockman Hole North field, previously a target of the Spitzer Wide-area Infrared Extragalactic (SWIRE) survey and extremely deep 20 cm mapping with the Very Large Array, which we have obtained using the Max-Planck millimeter bolometer (MAMBO) array on the IRAM 30 m telescope. After filtering, our full map has an RMS sensitivity ranging from 0.45 to 1.5 mJy/beam, with an average of 0.75 mJy/beam. Using the pixel flux distribution in a map made from our best data, we determine the shape, normalization, and approximate flux density cutoff for 1.2 mm number counts well below our nominal sensitivity and confusion limits. After validating our full dataset through comparison with this map, we successfully detect 41 1.2 mm sources with S/N > 4.0 and S(1.2 mm)\simeq 2-5 mJy. We use the most significant of these detections to directly determine the integral number counts down to 1.8 mJy, which are consistent with the results of the pixel flux distribution analysis. 93% of our 41 individual detections have 20 cm counterparts, 49% have Spitzer/MIPS 24 micron counterparts, and one may have a significant Chandra X-ray counterpart. We resolve \simeq 3% of the cosmic infrared background (CIB) at 1.2 mm into significant detections, and directly estimate a 0.05 mJy faint-end cutoff for the counts that is consistent with the full intensity of the 1.2 mm CIB. The median redshift of our 17 detections with spectroscopic or robust photometric redshifts is z(median)=2.3, and rises to z(median)=2.9 when we include redshifts estimated from the radio/far-infrared spectral index. By using a nearest neighbor and angular correlation function analysis, we find evidence that our S/N>4.0 detections are clustered at the 95% confidence level.

Quantum phase transition in the one-dimensional extended quantum compass model in a transverse field

Quantum phase transitions in the one-dimensional extended quantum compass model in a transverse field are studied by using the Jordan-Wigner transformation. This model is always gapful, except at the critical surfaces where the energy gap disappears. We obtain the analytic expressions of all critical fields which drive quantum phase transitions. This model shows a rich phase diagram which includes spin-flop, strip antiferromagnetic, and saturated ferromagnetic phases in addition to the phase with antiparallel ordering of the $y$ spin component on odd bonds. We also study also the universality and scaling properties of the transverse susceptibility and nearest-neighbor correlation function derivatives in different regions to confirm the results obtained using the energy gap analysis.

Two Point Correlation Functions for a Periodic Box-Ball System

We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific $N$-point functions is also presented.

Correlation functions for the three-state superintegrable chiral Potts spin chain of finite lengths

We compute the correlation functions of the three-state superintegrable chiral Potts spin chain for chains of length 3, 4, 5. From these results we present conjectures for the form of the nearest-neighbor correlation function.

Mott-Hubbard versus charge-transfer behavior inLaSrMnO4studied via optical conductivity

figuration 10Dq= 1.2 eV, eg= 1.4 eV, and t2g = 0.2 eV. The spectral weight of the lowest absorption feature at 1 – 2 eV changes by a factor of 2 as a function of temperature, which can be attributed to the change of the nearest-neighbor spin-spin correlation function across the Neel temperature TN = 133 K. Interpreting LaSrMnO4 effectively as a Mott-Hubbard insulator naturally explains this strong temperature dependence, the relative weight of the different absorption peaks, and the pronounced anisotropy. By means of transmittance measurements, we determine the onset of the optical gap opt = 0.4– 0.45 eV at 15 K and 0.1– 0.2 eV at 300 K. Our data show that the crystal-field splitting is too large to explain the anomalous temperature dependence of the c-axis lattice parameter by thermal occupation of excited crystal-field levels. Alternatively, we propose that a thermal population of the upper Hubbard band gives rise to the shrinkage of the c-axis lattice parameter.

Spin diffusion and the anisotropic spin-12Heisenberg chain

Measurements of the spin-lattice relaxation rate $1∕{T}_{1}$ by nuclear magnetic resonance for the one-dimensional Heisenberg antiferromagnet ${\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{3}$ have provided evidence for a diffusionlike contribution at finite temperature and small wave vector. By analyzing real-time data for the auto- and nearest-neighbor spin-spin correlation functions obtained by the density-matrix renormalization group I show that such a contribution indeed exists for temperatures $T>J$, where $J$ is the coupling constant, but that it becomes exponentially suppressed for $T⪡J$. I present evidence that the frequency dependence of $1∕{T}_{1}$ in the Heisenberg case is smoothly connected to that in the free fermion case where the exponential suppression of the diffusionlike contribution is easily understood.