Long-range Correlation Functions Research Articles

Interacting Colour Strings Approach in Modelling of Rapidity Correlations

In this paper, using the concept of multi-pomeron exchange, we develope a Monte Carlo model of interacting quark–gluon strings acting as particle-emitting sources aimed at describing inelastic proton–proton interactions at high energies. The implemented 3D (three-dimensional) dynamics of colour string formation resulted in their finite length in the rapidity space and in the fluctuating event-by-event spatial density. Thus, this results in string cluster formation because of the fusion mechanism and the appearance of long-range multiplicity and mean transverse momentum (mean-pT) correlations in rapidity. We study, via the pseudorapidity dependence, the sensitivity to the details of the 3D dynamical formation of strings for several observables such as the forward–backward correlation coefficient value, strongly intensive quantity, Σ, and the “almost” strongly intensive observable, the variance, σC2, of the distribution of the asymmetry coefficient, C. The strongly intensive quantity Σ is used in this study to suppress trivial statistical fluctuations in the number of particles emitting similar types of sources and to reveal the intrinsic fluctuations of a single source. We demonstrate the connection between Σ and such often used observables as cumulants, factorial cumulants, and σC2. We stress the importance of the contribution of “short” strings and the event asymmetry of the initial conditions on the long-range correlation measures. We argue that string cluster formation because of the fusion mechanism explains the collective effects seen in multiplicity and transverse momentum–multiplicity, ⟨pT⟩–N, long-range correlation functions.

Multifractal characterization as a function of timescale in the light curves with planetary signal observed by the Kepler mission

We investigate the evolution of five multifractal indicators of the Kepler Mission light curves of the moderately young Sun-like Kepler-30 star accompanied by a three-planet system. We focus not only on the fact that the rotational modulation has multifractality properties but also on some studies on these properties based on scale. Then, we systematically investigate the dynamic behaviors of the small and large fluctuations in two types of light curves (PDC and SAP). Those fluctuations indicate that the properties of stellar noise and rotation modulation are highlighted when we apply the Multifractal Detrended Moving Average (MFDMA) algorithm. Our results also demonstrated that the multifractality of the light curve is due to both long-range correlation and broad probability density function, but the main source of multifractality is the long-range correlation. This new approach can be used to develop theoretical and computational models for various stellar magnetic activity-related phenomena and their interactions with the planets, and it can greatly simplify spot modeling from current TESS and future PLATO data.

Quantum phase transition in a non-Hermitian XY spin chain with global complex transverse field

In this work, we investigate the quantum phase transition in a non-Hermitian XY spin chain. The phase diagram shows that the critical points of Ising phase transition expand into a critical transition zone after introducing a non-Hermitian effect. By analyzing the non-Hermitian gap and long-range correlation function, one can distinguish different phases by means of different gap features and decay properties of correlation function, a tricky problem in traditional XY model. Furthermore, the results reveal the relationship among different regions of the phase diagram, non-Hermitian energy gap and long-range correlation function.

Impurity-driven transitions in frustrated quantum Ising rings.

We study the quantum phase transition driven by a point impurity in a chain seamed with ring frustration. With strong coupling and light impurity, the system is in a topological extended-kink (TEK) phase, which exhibits gapless excitations in the bulk. With strong coupling and heavy impurity, the system is in a gapped kink bound state (KBS) phase. Two-point bulk and impurity correlations are defined to characterize the two phases. In the TEK phase, both the bulk and impurity correlations are long range and factorizable so that scaling functions can be parsed. The scaling functions relies on the distance scaled by the system's size. An impurity correlation length can be extracted from the impurity correlation. In the transition from TEK to KBS, the scaling function of the bulk correlation undergoes an abrupt steplike change. Meanwhile, the impurity correlation length decreases from a divergent value to a finite one. The ground state of the TEK phase retains a relatively high value of entanglement entropy due to the absence of symmetry breaking. However, spontaneous symmetry breaking occurs in the KBS phase, which induces antiferromagnetic order in the bulk and entangled spin configuration near the impurity.

Machine-Learning Studies on Spin Models

With the recent developments in machine learning, Carrasquilla and Melko have proposed a paradigm that is complementary to the conventional approach for the study of spin models. As an alternative to investigating the thermal average of macroscopic physical quantities, they have used the spin configurations for the classification of the disordered and ordered phases of a phase transition through machine learning. We extend and generalize this method. We focus on the configuration of the long-range correlation function instead of the spin configuration itself, which enables us to provide the same treatment to multi-component systems and the systems with a vector order parameter. We analyze the Berezinskii-Kosterlitz-Thouless (BKT) transition with the same technique to classify three phases: the disordered, the BKT, and the ordered phases. We also present the classification of a model using the training data of a different model.

Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring

On a ring, a single Jordan-Wigner transformation between the Kitaev model and the spin model suffers redundant degrees of freedom. However, we can establish an exact quaternary Jordan-Wigner mapping involving two Kitaev rings and two spin rings with periodic or antiperiodic boundary conditions. This mapping facilitates us to demonstrate exactly how a topological extended-kink (TEK) phase develops in the interacting Kitaev ring with odd number of lattice sites. The emergence of this new phase is attributed to the effect of geometrical ring frustration. Unlike the usual topological phases protected by energy gap in noninteracting systems, the TEK phase is gapless. And because the spectra of low energy excitations are quadratic, the specific heat per site approaches a half of Boltzmann constant near absolute zero temperature. More interestingly, the ground state is unique, immune to spontaneous symmetry breaking. It exhibits a long-range correlation function with a nonlocal factor, but no local order parameter can be defined. As a concomitant effect, a special kind of localized kink zero mode (KZM) takes place if we introduce a type of bond defect. We also show that the KZM is robust against moderate disorders.

Association between Multiscale Entropy Characteristics of Heart Rate Variability and Ischemic Stroke Risk in Patients with Permanent Atrial Fibrillation

Multiscale entropy (MSE) profiles of heart rate variability (HRV) in patients with atrial fibrillation (AFib) provides clinically useful information for ischemic stroke risk assessment, suggesting that the complex properties characterized by MSE profiles are associated with ischemic stroke risk. However, the meaning of HRV complexity in patients with AFib has not been clearly interpreted, and the physical and mathematical understanding of the relation between HRV dynamics and the ischemic stroke risk is not well established. To gain a deeper insight into HRV dynamics in patients with AFib, and to improve ischemic stroke risk assessment using HRV analysis, we study the HRV characteristics related to MSE profiles, such as the long-range correlation and probability density function. In this study, we analyze the HRV time series of 173 patients with permanent AFib. Our results show that, although HRV time series in patients with AFib exhibit long-range correlation (1/f fluctuations)—as observed in healthy subjects—in a range longer than 90 s, these autocorrelation properties have no significant predictive power for ischemic stroke occurrence. Further, the probability density function structure of the coarse-grained times series at scales greater than 2 s is dominantly associated with ischemic stroke risk. This observation could provide valuable information for improving ischemic stroke risk assessment using HRV analysis.

Structural correlation in water probed by hyper-Rayleigh scattering.

Second-harmonic or hyper-Rayleigh scattering (HRS) is sensitive to molecular interactions and correlations, and there is a large coherent HRS contribution for water. This work shows that the distinctive angle and polarization dependence observed for HRS from water is due to the long-range orientation correlation of the molecules. The results of HRS experiments for water are analyzed in combination with a molecular dynamics simulation to determine the molecular hyperpolarizability and the short-range and long-range orientation correlation functions for the molecules. At long range, the longitudinal and transverse dipole-dipole orientation correlation functions are BL(r) = -2BT(r) = a3/r3 with a = 0.166 nm. Molecular correlation at distances r > 100 nm must be included to account for the HRS observations.

Twisted superfluid phase in the extended one-dimensional Bose-Hubbard model

In one-dimensional systems a twisted superfluid phase is found which is induced by a spontaneous breaking of the time-reversal symmetry. Using the density-matrix renormalization group allows us to show that the excitation energy gap closes exponentially causing a quasi-degenerate ground state. The two degenerate ground states are connected by the time-reversal symmetry which manifests itself in an alternating complex phase of the long-range correlation function. The quantum phase transition to the twisted superfluid is driven by pair tunneling processes in an extended Bose-Hubbard model. The phase boundaries of several other phases are discussed including a supersolid, a pair superfluid, and a pair supersolid phase as well as a highly unconventional Mott insulator with a degenerate ground state and a staggered pair correlation function.

Strangeness production and long-range correlations in pp collisions in string fusion approach

The effects of string fusion on the correlations in strange particles production in proton-proton collisions at high energy are studied in the framework of a Monte Carlo string-parton model. The model is based on the strings formation in elementary dipole-dipole collisions. The hardness of the elementary interaction is defined by a transverse size of the colliding dipoles. The interaction between strings is realized in the accordance with the string fusion model prescriptions by the introduction of the lattice in the impact parameter plane and taking into account the finite rapidity length of strings. The particles species differentiation is implemented according to Schwinger mechanism. The parameters of the model are fixed with the experimental data on total inelastic cross section and charged multiplicity. In the framework of the model the long-range correlation functions with an accounting of strangeness have been studied. A new intensive event-by-event observable has been proposed, which characterizes the fraction of strange particles in the event. The predictions on the correlations between strangeness, multiplicity and mean transverse momentum are obtained for pp collisions at 7 TeV.

Short-range interactions versus long-range correlations in bird flocks.

Bird flocks are a paradigmatic example of collective motion. One of the prominent traits of flocking is the presence of long range velocity correlations between individuals, which allow them to influence each other over the large scales, keeping a high level of group coordination. A crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations. Here we use the maximum entropy (ME) approach to infer from experimental data of natural flocks the effective interactions between individuals. Compared to previous studies, we make a significant step forward as we retrieve the full functional dependence of the interaction on distance, and find that it decays exponentially over a range of a few individuals. The fact that ME gives a short-range interaction even though its experimental input is the long-range correlation function, shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters. Finally, we show how the method can be used to capture the degree of anisotropy of mutual interactions.

Particle correlations and their implication to collectivity in pPb and PbPb from CMS

The long-range two-particle correlation functions reveal the near-side ridge structures in highmultiplicity pp, pPb and PbPb collisions at the Large Hadron Collider (LHC). The model that takes into account the collective flow originated from the initial-state geometry fluctuation can successfully describe the measured long-range correlation functions of charged particles. In this review paper, the recent experimental data on the long-range correlations and the extracted elliptic and triangular flow parameters in pPb and PbPb collisions from the Compact Muon Solenoid (CMS) experiment are summarized. The flow parameters from the longrange correlation analyses are compared with those from the multiparticle cumulants and the Lee-Yang Zeros (LYZ) method. In addition, the pseudorapidity dependence of long-range two-particle correlation functions in pPb and the deduced flow parameters for identified strange hadrons (K S 0 and Λ/Λ) in pPb and PbPb are also presented to provide more insights on the long-range correlations and flow dynamics.

双层哈伯德模型中激子态的数值研究

本文采用约束路径量子蒙特卡罗方法系统地探讨了双层哈伯德模型中的激子态特性。计算结果表明，当空穴和电子掺杂浓度低于0.08时，由层间单粒子隧穿强度表征的局域激子态被层间库仑相互作用V增强，且随着掺杂浓度的减小增强效应逐渐变强，而当空穴和电子掺杂浓度高于0.08时，局域激子态却被V减弱。该结果与已发表的有限温度结果存在重要的差异。进一步的分析发现在整个掺杂区间，激子的长程空间关联函数随着V的增加而减小，表明研究的双层哈伯德模型中不存在激子序参量的长程序，即激子凝聚态。此外，层间库仑相互作用V对格点磁矩的影响很小。 This work investigates the exciton property of the bilayer Hubbard model by using the con-strained-path Monte Carlo method. The calculated results show that when the doping density is lower than 0.08, the local exciton characterized by interlayer single particle tunneling is enhanced by the interlayer Coulomb interaction V, and the enhancement becomes stronger with decreasing the doping density. However, when the doping density is higher than 0.08, the local exciton is sup- pressed by V. This result exhibits significant differences from the published results at finite temperatures. Further analysis shows that the long-range exciton correlation function is reduced with increasing V, demonstrating that there does not exist exciton condensation in the studied model. In addition, the interlayer Coulomb interaction V is shown to have a rather weak effect on local magnetic moment.

EXACT GROUND STATES OF CORRELATED ELECTRONS ON PENTAGON CHAINS

We construct a class of exact ground states for correlated electrons on pentagon chains in the high density region and discuss their physical properties. In this procedure the Hamiltonian is first cast in a positive semidefinite form using composite operators as a linear combination of creation operators acting on the sites of finite blocks. In the same step, the interaction is also transformed to obtain terms which require for their minimum eigenvalue zero at least one electron on each site. The transformed Hamiltonian matches the original Hamiltonian through a nonlinear system of equations whose solutions place the deduced ground states in restricted regions of the parameter space. In the second step, nonlocal product wave functions in position space are constructed. They are proven to be unique ground states which describe non-saturated ferromagnetic and correlated half metallic states. These solutions emerge when the strength of the Hubbard interaction Ui is site-dependent inside the unit cell. In the deduced phases, the interactions tune the bare dispersive band structure such to develop an effective upper flat band. We show that this band flattening effect emerges for a broader class of chains and is not restricted to pentagon chains. For the characterization of the deduced solutions, uniqueness proofs, exact ground state expectation values for long-range hopping amplitudes and correlation functions are also calculated. The study of physical reasons which lead to the appearance of ferromagnetism has revealed a new mechanism for the emergence of an ordered phase, described here in detail. This works as follows: starting from a completely dispersive bare band structure, the interactions quench the kinetic energy, hence the ordered phase is obtained solely by a drastic decrease of the interaction energy. Since Ui are site dependent, this determinative decrease is obtained by a redistribution of the double occupancy di such to attain small di where the on-site Coulomb repulsion Ui is high, and vice versa. The kinetic energy quench leads to the upper effective flat band, whose role is to enhance by its degeneracy the switching to the ordered phase dictated and stabilized by the interactions present. It is shown that for this phenomenon to occur, a given degree of complexity is needed for the chain, and the mechanism becomes inactive when the Ui interactions are homogeneous, or are missing from the ground state wave function.

Harmonic decomposition of two particle angular correlations in Pb–Pb collisions at [formula omitted

Angular correlations between unidentified charged trigger (t) and associated (a) particles are measured by the ALICE experiment in Pb–Pb collisions at sNN=2.76 TeV for transverse momenta 0.25<pTt,a<15 GeV/c, where pTt>pTa. The shapes of the pair correlation distributions are studied in a variety of collision centrality classes between 0 and 50% of the total hadronic cross section for particles in the pseudorapidity interval |η|<1.0. Distributions in relative azimuth Δϕ≡ϕt−ϕa are analyzed for |Δη|≡|ηt−ηa|>0.8, and are referred to as “long-range correlations”. Fourier components VnΔ≡〈cos(nΔϕ)〉 are extracted from the long-range azimuthal correlation functions. If particle pairs are correlated to one another through their individual correlation to a common symmetry plane, then the pair anisotropy VnΔ(pTt,pTa) is fully described in terms of single-particle anisotropies vn(pT) as VnΔ(pTt,pTa)=vn(pTt)vn(pTa). This expectation is tested for 1⩽n⩽5 by applying a global fit of all VnΔ(pTt,pTa) to obtain the best values vn{GF}(pT). It is found that for 2⩽n⩽5, the fit agrees well with data up to pTa∼3–4 GeV/c, with a trend of increasing deviation as pTt and pTa are increased or as collisions become more peripheral. This suggests that no pair correlation harmonic can be described over the full 0.25<pT<15 GeV/c range using a single vn(pT) curve; such a description is however approximately possible for 2⩽n⩽5 when pTa<4 GeV/c. For the n=1 harmonic, however, a single v1(pT) curve is not obtained even within the reduced range pTa<4 GeV/c.

Triggered di-hadron correlations in Pb–Pb collisions from the ALICE experiment

Angular correlations between trigger (t) and associated (a) hadrons are measured by the ALICE experiment for 0.5 < pt, aT < 15 GeV, where ptT ⩾ pTa. The azimuthal pair correlation shapes are examined in a variety of centrality categories for pairs in |η| < 1.0 where |ηt − ηa| > 0.8. A series of two-particle Fourier components VnΔ ≡ ⟨cos (nΔϕ)⟩ are extracted from the long-range azimuthal correlation functions. The sum of n < 6 terms matches the data. For each n, a fit is applied over all pT bins simultaneously to test the collectivity hypothesis VnΔ ≃ vtn van. The factorization holds at pt, aT below approximately 4 GeV but breaks progressively at higher momenta. The divergence between the data and the global fit quantifies the onset of nonflow dominance in long-range correlations due to the away side jet. The vn values from the global fit are in close agreement with results from more established methods. At higher pT where jet correlations dominate, the modification of conditional yields in central Pb–Pb collisions is measured with respect to pp (IAA) and with respect to peripheral events (ICP). Significant suppression is observed on the side opposing the trigger, while a moderate enhancement is measured on the near side.

Unified description of long-time tails and long-range correlation functions for sheared granular liquids

Unified description on the long-time tail of velocity autocorrelation function (VACF) and the algebraic decays of the equal-time spatial correlation functions for nearly elastic and uniformly sheared granular liquids is developed based on the generalized fluctuating hydrodynamics. We predict that the cross-over of the long-time tail of VACF from t−3/2 to t−5/2 with the time t regardless of the density. We also demonstrate the existence of algebraic tails of the equal-time spatial density correlation function and the equal-time spatial velocity correlation function which respectively satisfy r−11/3 and r−5/3 for large distance r.

Exact algorithm for sampling the two-dimensional Ising spin glass

A sampling algorithm is presented that generates spin-glass configurations of the two-dimensional Edwards-Anderson Ising spin glass at finite temperature with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow dynamics of direct simulation and can be used to study long-range correlation functions and coarse-grained dynamics. The algorithm uses a correspondence between spin configurations on a regular lattice and dimer (edge) coverings of a related graph: Wilson's algorithm [D. B. Wilson, Proceedings of the Eighth Symposium on Discrete Algorithms (SIAM, Philadelphia, 1997), p 258] for sampling dimer coverings on a planar lattice is adapted to generate samplings for the dimer problem corresponding to both planar and toroidal spin-glass samples. This algorithm is recursive: it computes probabilities for spins along a "separator" that divides the sample in half. Given the spins on the separator, sample configurations for the two separated halves are generated by further division and assignment. The algorithm is simplified by using Pfaffian elimination rather than Gaussian elimination for sampling dimer configurations. For n spins and given floating point precision, the algorithm has an asymptotic run-time of O(n(3/2)); it is found that the required precision scales as inverse temperature and grows only slowly with system size. Sample applications and benchmarking results are presented for samples of size up to n=128(2), with fixed and periodic boundary conditions.

Classical to quantum mappings for geometrically frustrated systems: Spin-ice in a [100] field

Certain classical statistical systems with strong local constraints are known to exhibit Coulomb phases, where long-range correlation functions have power-law forms. Continuous transitions from these into ordered phases cannot be described by a na\"{\i}ve application of the Landau--Ginzburg--Wilson theory since neither phase is thermally disordered. We present an alternative approach to a critical theory for such systems, based on a mapping to a quantum problem in one fewer spatial dimensions. We apply this method to spin-ice, a magnetic material with geometrical frustration, which exhibits a Coulomb phase and a continuous transition to an ordered state in the presence of a magnetic field applied in the [100] direction.

Measurement-based quantum computation beyond the one-way model

We introduce schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in Gross and Eisert [Phys. Rev. Lett. 98, 220503 (2007); quant-ph/0609149]. Our method makes use of tools from many-body physics-matrix product states, finitely correlated states, or projected entangled pairs states-to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem-how to realize quantum computation-was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting and present a large number of examples. We find computational schemes, which differ from the original one-way computer, for example, in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may, for example, exhibit nonvanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev's toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.