Short-range Correlation Functions Research Articles

Thermodynamics of resonating-valence-bond states toward the understanding of quantum spin liquid phenomena.

A quantum spin liquid (QSL) is a state of matter in which spins do not exhibit magnetic order. In contrast to paramagnets, the spins in a QSL interact strongly, similar to conventional ordered magnets; however the thermodynamic stability of QSLs is rarely studied. Here, the thermodynamic properties of centered hexagon nanoclusters were investigated using the Hubbard model, which was solved using exact numerical diagonalization. The total spin, spin-spin correlation functions, local magnetic moments, charge and spin gaps, and magnetocaloric effect were analyzed for a half-filled band as a function of the ratio between the on-site Coulomb repulsion and electronic hopping (U/t). The centered hexagon nanocluster exhibited an antiferromagnetic (AFM) behavior with exotic magnetic ordering. Resonating-valence-bond (RVB) states were observed for intermediate values of U/t, in which short-range spin-spin correlation functions were suppressed to minimize spin frustration. The AFM order was examined in terms of the Néel-like temperature derived from the temperature dependence of the magnetic susceptibility. An interesting result is that the systems under external magnetic fields exhibited an inverse magnetocaloric effect, which was remarkable for intermediate values of U/t, where the RVB state was observed. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene (TBLG) systems, these results provide insights into the onset of magnetism and the possible spin liquid states in these graphene moiré materials.

Fourth-neighbour two-point functions of the XXZ chain and the fermionic basis approach

We give a descriptive review of the fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way that allows for their direct implementation on a computer. Within the fermionic basis approach a huge class of stationary reduced density matrices, compatible with the integrable structure of the model, assumes a factorized form. This means that all expectation values of local operators and all two-point functions, in particular, can be represented as multivariate polynomials in only two functions ρ and ω and their derivatives with coefficients that are rational in the deformation parameter q of the model. These coefficients are of ‘algebraic origin’. They do not depend on the choice of the density matrix, which only impacts the form of ρ and ω. As an example we work out in detail the case of the grand canonical ensemble at temperature T and magnetic field h for q in the critical regime. We compare our exact results for the fourth-neighbour two-point functions with asymptotic formulae for h, T = 0 and for finite h and T.

Holographic derivation of a class of short range correlation functions

We construct a class of backgrounds with a warp factor and anti-de Sitter asymptotics, which are dual to boundary systems that have a ground state with a short-range two-point correlation function. The solutions of probe scalar fields on these backgrounds are obtained by means of confluent hypergeometric functions. The explicit analytical expressions of a class of short-range correlation functions on the boundary and the correlation lengths ξ are derived from gravity computation. The two-point function calculated from gravity side is explicitly shown to exponentially decay with respect to separation in the infrared. Such feature inevitably appears in confining gauge theories and certain strongly correlated condensed matter systems.

Electron scattering from some even fp- and N50-shell nuclei with implanting the influence of short-range correlation functions

The influence of two body short range correlations on elastic electron scattering charge form factors, charge densities as well as root mean square charge radii of some fp-shell nuclei (for example, 48Ca, 50Cr, 54Fe, 58Ni, 70Ge and 74Se) and some N50-shell nuclei (for example, 88Sr and 90Zr) is analyzed using the one- and two-body terms in the cluster expansion together with the single particle harmonic oscillator wave functions. The Jastrow-type correlation function is utilized to embed the effect of short range correlations into elastic charge form factors F(q) and charge densities ρ(r). Both F(q) and ρ(r) depend upon the harmonic oscillator parameter b and the correlation parameter β (which initiates from the Jastrow correlation function). Here, the parameters b and β are determined via the fitting to the measured charge form factors. The embedding of short range correlations imitates the measured charge form factors at the high momentum transfers (q ≥ 2 fm−1). It is noticed that the implanting of short range correlations is required for obtaining a remarkable alteration in the computed elastic charge form factors which in turn leads to explain the data of electron scattering astonishingly throughout the entire range of considered momentum transfers.

Correlation functions of the integrable spin chain

We study the correlation functions of , n > 2, invariant spin chains in the thermodynamic limit. We formulate a consistent framework for the computation of short-range correlation functions via functional equations which hold even at finite temperature. We give the explicit solution for two- and three-site correlations for the case at zero temperature. The correlators do not seem to be of factorizable form. From the two-site result we see that the correlation functions are given in terms of Hurwitz’s zeta function, which differs from the case where the correlations are expressed in terms of Riemann’s zeta function of odd arguments.

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.

Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model

Optical lattice experiments with ultracold fermion atoms and quantum gas microscopy have recently realized direct measurements of magnetic correlations at the site-resolved level. We calculate the short-range spin-correlation functions in the ground state of the two-dimensional repulsive Hubbard model with the auxiliary-field quantum Monte Carlo (AFQMC) method. The results are numerically exact at half filling where the fermion sign problem is absent. Away from half filling, we employ the constrained path AFQMC approach to eliminate the exponential computational scaling from the sign problem. The constraint employs unrestricted Hartree-Fock trial wave functions with an effective interaction strength $U$, which is optimized self-consistently within AFQMC. Large supercells are studied, with twist averaged boundary conditions as needed, to reach the thermodynamic limit. We find that the nearest-neighbor spin correlation always increases with the interaction strength $U$, contrary to the finite-temperature behavior where a maximum is reached at a finite $U$ value. We also observe a change of sign in the next-nearest-neighbor spin correlation with increasing density, which is a consequence of the buildup of the long-range antiferromagnetic correlation. We expect the results presented in this paper to serve as a benchmark as lower temperatures are reached in ultracold atom experiments.

Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, 3H and 4He, using the nucleon–nucleon interaction AV8′. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.

Paramagnetic susceptibility and correlation functions of a [formula omitted]-dimensional classical Heisenberg ferromagnet via the two-time Green function method

In the present paper we investigate the paramagnetic susceptibility and the short-range order correlation functions of a d-dimensional classical isotropic ferromagnetic Heisenberg model with short-range exchange interactions by employing the two-time Green function method in classical statistical mechanics. Here we use Tyablikov–Callen-like decouplings for higher order Green functions and a formula for magnetization recently obtained by extension of the well known Callen method developed many years ago for the quantum isotropic Heisenberg model. Although our analysis is true for any temperature and dimensionality, we focus on one-, and some two- and three-dimensional lattices of experimental interest and derive asymptotic expressions for susceptibility and correlation functions within the paramagnetic phase close to the phase boundary and in the high-temperature regime. Besides, we present a Fourier series expansion method for deriving the high-temperature behaviors of the correlation functions. Our predictions, as obtained from a genuine classical many-body framework, may constitute a good reference point for the quantum counterparts emerging in the classical limit at the same level of approximation. Of course, although the classical spin models have unrealistic properties at sufficiently low temperatures, our classical analysis provides, in a relatively simple way as compared to a quantum treatment, an experimentally interesting scenario at finite temperature and dimensionalities d≥1.

Short-range two-particle correlations from statistical clusters

The two-particle short-range correlation functions in rapidity, azimuthal angle, and transverse momentum following from the decay of statistical clusters are evaluated and discussed.Received 2 September 2015DOI:https://doi.org/10.1103/PhysRevD.93.094015© 2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFragmentation into hadronsParticle productionParticles & Fields

Inelastic electron scattering from light nuclei

The inelastic longitudinal form factors F(q) ’s, an expression for the transition charge density were studied where the deformation in nuclear collective modes besides the shell model transition density are taken into consideration. In this work, the core polarization transition density was evaluated by adopting the shape of Tassie model together with the form of the ground state two-body charge density distributions and the effect of two body short range correlation function. It was noticed that the core polarization effects, which represent the collective modes are essential in obtaining a good agreement between the calculated inelastic longitudinal F(q) ’s and those of the experimental data for 4He, 12C, 16O, 28Si, 32S and 40Ca nuclei. J.Natn.Sci.Foundation Sri Lanka 2013 41 (3): 209-217 DOI: http://dx.doi.org/10.4038/jnsfsr.v41i3.6053

Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.

Influence of dipole–dipole correlations on the stability of the biaxial nematic phase in the model bent-core liquid crystal

A molecular theory of biaxial nematic ordering in the system of bent-core molecules has been developed in the two-particle cluster approximation which enables one to take into account short-range polar correlations determined by both electrostatic dipole–dipole interaction and polar molecular shape. All orientational order parameters and short-range correlation functions are calculated numerically as functions of temperature in the uniaxial and in the biaxial nematic phases, and the results are compared with the ones obtained in the mean-field approximation and in the cluster approximation but without taking into consideration the dipole–dipole interaction. It is shown that short-range polar correlations and, in particular, the dipole–dipole correlations dramatically increase the temperature of the transition into the biaxial nematic phase and enhancing its stability range. The results are also very sensitive to the value of the opening angle of a model bent-core molecule.

Thermodynamics and short-range correlations of theXXZ chain close to its triple point

The XXZ quantum spin chain has a triple point in its ground stateh–1/Δ phase diagram. This first order critical point is located at the joint end point of the twosecond order phase transition lines marking the transition from the gapless phase tothe fully polarized phase and to the Néel ordered phase, respectively. We explorethe magnetization and the short-range correlation functions in its vicinity usingthe exact solution of the model. In the critical regime above the triple point weobserve a strong variation of all physical quantities on a low energy scale of order1/Δ induced by the transverse quantum fluctuations. We interpret this phenomenon startingfrom a strong coupling perturbation theory around the highly degenerate ground state ofthe Ising chain at the triple point. From the perturbation theory we identify the relevantscaling of the magnetic field and of the temperature. Applying the scaling to the exactsolutions we obtain explicit formulae for the magnetization and short-range correlationfunctions at low temperatures.

Fractal Substructure of a Nanopowder

The structural evolution of a nanopowder by repeated dispersion and settling can lead to characteristic fractal substructures. This is shown by numerical simulations of a two-dimensional model agglomerate of adhesive rigid particles. The agglomerate is cut into fragments of a characteristic size l, which then are settling under gravity. Repeating this procedure converges to a loosely packed structure, the properties of which are investigated: (a) The final packing density is independent of the initialization, (b) the short-range correlation function is independent of the fragment size, (c) the structure is fractal up to the fragmentation scale l with a fractal dimension close to 1.7, and (d) the relaxation time increases linearly with l.

Behavior of a Bose-Einstein condensate containing a large number of atoms interacting through a finite-range interatomic interaction

We investigate Bose-Einstein condensates (BEC) containing a large number of bosonic atoms interacting via a finite-range semirealistic interatomic interaction. Ground state properties for an increasing number of atoms in the condensate have been calculated using a modification of the potential harmonic expansion method (including a short range correlation function in the expansion basis) to solve the many-body Schr\"odinger equation. An improved numerical algorithm for the calculation of the potential matrix elements permits us to have up to 14 000 atoms in the condensate. Although our approach is approximate and justified for dilute condensates, our results agree well with available diffusion Monte Carlo results for the same case. The ground state energies also agree well with those by the Gross-Pitaevskii equation method for up to 100 particles in the trap and become gradually larger than the latter (up to 5% for 14 000 atoms). The difference is attributed to the effects of finite range interatomic interaction and two-body correlations. Our approach presents a clear physical picture of the condensate, being computationally economical at the same time.

Partial phonon densities of states ofFe57in Fe-Cr: Analysis by a local-order cluster expansion

Nuclear resonant inelastic x-ray scattering spectra were measured for $^{57}\mathrm{Fe}$ in disordered body-centered-cubic alloys of Fe-Cr. Partial phonon density of states (DOS) curves were obtained from these data. These results, in conjunction with the results of Ruckert et al. [Hyperfine Interact. 126, 363 (2000)] on Fe-Cr thin-film multilayers and alloys, were analyzed with a local-order cluster expansion method. Interaction partial phonon DOS functions for the different short-range correlation functions were obtained from the disordered alloys. These interaction DOS functions were used in reconstructing the $^{57}\mathrm{Fe}$ partial DOS curves measured by Ruckert et al. on a set of thin-film multilayer samples of $^{57}\mathrm{Fe}∕^{56}\mathrm{Fe}∕\mathrm{Cr}$. The method worked well using terms up to a combined first- and second-nearest-neighbor triangle cluster, which were obtained reliably from the disordered alloys. The limitations of a basis set of correlation functions from disordered alloys are discussed but shown to be acceptable for the chemical trends of phonons in the Fe-Cr system.

A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain

Göhmann, Klümper and Seel derived the multiple integral formula of the density matrix of the XXZ Heisenberg chain at finite temperatures. We have applied the high temperature expansion (HTE) method to isotropic case of their formula in a finite magnetic field and obtained coefficients for several short-range correlation functions. For example, we have succeeded to obtain the coefficients of the HTE of the third neighbor correlation function 〈 σ j z σ j + 3 z 〉 for zero magnetic field up to the order of 25. These results expand our previous results on the emptiness formation probability [Z. Tsuboi, M. Shiroishi, J. Phys. A: Math. Gen. 38 (2005) L363–L370, condmat/0502569.] to more general correlation functions.

Short- and intermediate-range structural correlations in amorphous silicon carbide: A molecular dynamics study

Short- and intermediate-range structural correlations in amorphous silicon carbide $(\mathrm{a}\text{\ensuremath{-}}\mathrm{SiC})$ are studied in terms of partial pair distributions, bond angle distribution functions, and shortest-path ring statistics. A well relaxed sample is prepared following a slow annealing schedule of the simulation at the experimental density of the amorphous phase. The short-range correlation functions indicate a locally ordered amorphous structure with heteronuclear bonds, $\mathrm{Si}--\mathrm{C}$, with no phase separation, and no graphitic or diamond structures present. The bond distances and coordination numbers are similar to those in the crystalline phase. The rings statistics indicate an intermediate-range topology formed by the rearrangement of tetrahedra with the occurrence of corner and edge sharing units connecting two- ($\ensuremath{\sim}5%$ of total), three-, four-, and five-fold rings. The presence of large size rings indicates the existence of nano-voids in the structure, which explains the low density compared with the crystal phase while keeping the same coordination number and bond distance. These simulation results agree well with experimental results.

Power-law correlations and other models with long-range dependence on a lattice

This paper introduces long-range dependence for a stationary random field on a plane lattice, derives an exact power-law correlation model and other models with long-range dependence on the lattice, and explores the close connection between short-range dependent correlation functions and absolutely summable double sequences.