Nearest-neighbor Correlation Function Research Articles

Charge ordering in the extended Hubbard model in the ionic limit

We study the 1D extended Hubbard model in the ionic limit at zero temperature after the exact solution recently found by us [F. Mancini; Europhys. Lett. 70 (2005) 485]. In particular, we discuss the behavior of charge response functions (filling, double occupancy, nearest-neighbor correlation function) as functions of the ratio between positive on-site and intersite Coulomb interactions. This is equivalent to analyze spin-response functions as functions of the ratio between positive crystal field and negative exchange interaction in the 1D spin-1 Ising model in presence of an external magnetic field. We discuss the tendency to ordering shown by this exact solution.

Calculation of correlation functions in the Heisenberg spin-1/2 antiferromagnetic model

We derive the exact expression of the four-spinon contribution S 4 to the dynamical correlation function S of the spin 1/2 isotropic (XXX) He isenberg model in the antiferromagnetic regime using the quantum group symmetry of the model. We first give the exact expression for the n-spinon contribution in the form of contour integrals and display known results regarding the two-spinon contribution S 2. Then we specialize the n-spinon formula to the case n = 4 and compute three sum rules for S 4 that the total S is known to satisfy exactly. These are: the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that S 4 corrects only by a small amount the contribution from S 2.

Sum rules for four-spinon dynamic structure factor in XXX model

In the context of the antiferromagnetic spin 1 2 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor S 4 by calculating a number of sum rules the total dynamic structure factor S is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of S 4 is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor S 2 is between 70% and 75%. The calculations are numerical and Monte Carlo based. Good statistics are obtained.

Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic XXZ-chain at finite temperatures

We evaluate numerically certain multiple integrals representing nearest and next-nearest neighbor correlation functions of the spin-1/2 $XXZ$ Heisenberg infinite chain at finite temperatures.

Engineering antiferromagnetic Heisenberg spin chains for maximizing of the groundstate entanglement

We study the correlation function and concurrence for the eigenstates with zero spin of engineered Heisenberg models to explore the entanglement property. It is shown that the total nearest neighbor (NN) correlation function of zero-spin eigenstates reaches its local extremum when the coupling strength is uniform, and correspondingly the groundstate entanglement of d-D cubic AF Heisenberg model is locally maximized. Moreover, numerical calculations for a N-site quantum spin ring with cosinusoidally modulated exchange coupling, i.e., J i = J ( 1 + cos ( 2 π i / N ) ) , indicate that the uniform coupling is not the unique optimal distribution for maximizing the groundstate entanglement and this modulation of interactions can induce the longer range entanglement.

Next Nearest-Neighbor Correlation Functions of the Spin-1/2XXZChain at Massive Region

The second neighbor correlation functions of the spin-\(\frac{1}{2}\) X X Z chain in the ground state are expressed in the form of three dimensional integrals. We show that these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions for Δ>1.

Next-nearest-neighbour correlation functions of the spin-1/2XXZchain at the critical region

The correlation functions of the spin-1/2 XXZ spin chain in the ground state are expressed in the form of the multiple integrals. For -1< Delta <1, they were obtained by Jimbo and Miwa in 1996. Especially the next nearest-neighbour correlation functions are given as certain three-dimensional integrals. We shall show these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions. We have also found that the remaining one-dimensinal integrals can be evaluated analytically, when nu = arccos(Delta)/pi is a rational number.

Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series

We have extended through beta^{23} the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic lattices. Moreover the expansions for the nearest-neighbor correlation function, the susceptibility and the second correlation moment have been extended up to beta^{25}. Taking advantage of these new data, we can improve the accuracy of direct estimates of critical exponents and of hyper-universal combinations of critical amplitudes such as the renormalized four-point coupling g_r or the quantity usually denoted by R^{+}_{xi}. We have used a variety of series extrapolation procedures and, in some of the analyses, we have assumed that the leading correction-to-scaling exponent theta is universal and roughly known. We have also verified, to high precision, the validity of the hyperscaling relation and of the universality property both with regard to the lattice structure and to the value of the spin.

Formula omitted] alternating spin chains with Dzyaloshinskii–Moriya interaction

Using a fermion representation, we study the S= 1 2 one-dimensional anisotropic alternating Heisenberg model with a Dzyaloshinskii–Moriya (DM) antisymmetric exchange interaction normal to the xy-plane. For the uniform chain, we treat the four-fermion term in a Hartree–Fock approximation. We then calculate the ground state energy, the low-lying excitations and the static nearest-neighbor correlation functions in the T=0 limit. For the alternating chain, we calculate exactly the ‘spin-wave’ excitations in the XY limit.

Nearest-neighbor two-point correlation function of the Z-invariant eight-vertex model

The nearest-neighbor two-point correlation function of the Z-invariant inhomogeneous eight-vertex model in the thermodynamic limit is computed using the free-field representation.

Variational resonance valence bond study on the ground state of C60 using the Heisenberg model

A detailed variational resonance valence bond (RVB) study is performed for the S=0 ground state of the C60 molecule in the framework of the Heisenberg model. It is shown that the 12 500-dimensional Kekulé space can be divided into two subspaces of respective dimensions 5828 and 6672, of which the first one recovers 99.82% of the energy of the full Kekulé space. This 5828-dimensional subspace is derived from the main Kekulé function, which is formed from spin pairs on hexagon–hexagon bonds only, by simple rotations of the three spin pairs in disjoint sets of hexagonal rings of C60 in all possible ways. This indicates that the concept of the stability of the aromatic sextet still plays an important role even in this nonalternant system. Further, the inclusion of some longer range RVB functions like Dewar-type functions and functions involving Claus structures is investigated, and the effect on the ground-state energy as well as on the nearest neighbor correlation functions is examined.

Local magnetic moments induced by a nonmagnetic impurity in the two-dimensionalt−Jmodel

Local magnetic moments induced by a nonmagnetic impurity in the two-dimensional $t\ensuremath{-}J$ model are investigated by use of a Green function method in a finite-size system (50\ifmmode\times\else\texttimes\fi{}50=2500 sites). Local electron number and nearest-neighbor correlation functions are calculated self-consistently at each lattice point. A local electron number distribution shows that electrons form a bound state around an impurity site and the magnitude of the local moment is enhanced, whereas doped holes can be distributed only apart from the impurity site and destroy an antiferromagnetic spin configuration by their motion. This result is consistent with experimental results of Zn-doped high-${T}_{c}$ superconductors.

Cumulant calculations of thermodynamic quantities for the Hubbard and the emery model

The calculations of the first paper suggesting phase separation in the Hubbard model [2] are performed under modern computer facilties for the one and three-band Hubbard model. High-temperature approximations for specific heat and static correlation functions are obtained. The latter show, at these high temperatures, no tendency to phase separate in the same way as in the cited paper because our spin parallel nearest-neighbor charge correlation function is negative for all doping values. The spin antiparallel correlation function has positive and negative values for different doping regimes.

Self-consistent spin-spin and density-density correlations in the Hubbard model.

A linear combination of Hubbard projection operators is used to linearize the equations of motion for the Hubbard model. The Green's funtions in this linearization scheme depend explicitly on the value of the nearest-neighbor density-density correlation function. For the half-filled case we calculate this correlation function by taking variations of the equations of motion with respect to a density field. Three-body vertex corrections are ignored. The expressions we get for the correlation functions along with the equations of motion for the Green's functions form a system of equations that can be solved self-consistently. We solve these equations, both with and without effective vertex corrections, for a half-filled 12-site chain. These results are compared to numerically exact Lanczos solutions and to standard mean-field calculations. Calculations of on-site charge corelation, ground-state energy, and long-range spin-spin correlations for intermediate values of U show a significant improvement over standard mean-field techniques.

The half-filled Hubbard model in the pair approximation of the cluster variation method

The half filled Hubbard model is studied in the pair approximation of the Cluster Variation Method. The use of the $SO(4)$ symmetry of the model makes possible to give a complete analytical characterization of the ground state, by means of explicit expressions for the double occupancy and the nearest neighbor correlation functions. The finite temperature analysis is reduced to the numerical solution of only two coupled transcendental equations. The behavior of local magnetic moment, specific heat and correlation functions is given for some typical cases in one and two dimensions. We obtain good qualitative agreement with exact and numerical results in one dimension. The results for finite temperatures show a rapid evolution, with increasing temperature, from a strongly antiferromagnetic behavior to a disordered one; in the high temperature region a maximum (which has been related to a "gradual" metal--insulator transition) is found in the specific heat for very large values of the Coulomb repulsion.

Reactant segregation in a Langmuir–Hinshelwood surface reaction

We have performed Monte Carlo simulations of a Langmuir–Hinshelwood reaction between two species A and B adsorbed on a square lattice, with the goal of determining how spatial correlations between the species vary with reaction rate. Adsorption of each species occurs when a gas-phase molecule, either A or B, impinges upon a vacant lattice site. The probability that a molecule impinges upon and adsorbs successfully into a vacant lattice site per unit time is pa/2 for both species. Desorption is not allowed and the surface reaction is allowed to occur only between nearest-neighbor AB pairs. For each nearest-neighbor AB pair, the probability of reaction per unit time is pr. A novel feature of this investigation is that we explicitly simulate the diffusion of the particles on the lattice. The particles are allowed to migrate by hopping to vacant nearest-neighbor sites, where the probability of a hop per unit time is pm. In all these simulations we have set pm to be unity, and varied pr from 0.01 to unity. We have also set pa=pr/5 for all the simulations in order to maintain moderately low fractional surface coverages. ‘‘Islanding’’ of each type of particle occurs even for the lowest value of pr used, although the entire surface is never poisoned. For range of values of pr used, the ‘‘islands’’ grow to a finite steady-state size. We also found that the islands that are formed are consistent with a dimension of two. A nearest-neighbor correlation function φ is defined to describe the process of islanding, and the dependence of φ upon pm/pr is studied. By studying this simple model we show that quite large inhomogeneities can be reasonably expected to occur in catalytic systems even when reaction probabilities are small compared to diffusion rates, and that these inhomogeneities affect total reaction rates.

Study of correlation functions in molecular crystals

We have studied the correlation functions for a model Hamiltonian describing the vibrational properties in molecular crystals. The model Hamiltonian consists of terms characterizing the on-site anharmonicity and the nearest-neighbor hopping interaction. If the on-site anharmonicity is uniform, the correlation functions exhibit no structure. However, structure appears in the nearest-neighbor correlation function if the anharmonicity is nonuniform. Because the Hamiltonian resembles the Hubbard model for the electronic case, the implication of the results to high temperature superconductors is indicated.

Cooperative denaturation kinetics of homogeneous polymers

The kinetics of denaturation of a homogeneous, helical biopolymer with nearest neighbor interactions are described, using a kinetic Ising model in which the configuration of its neighbors dictates the transition probability for a single residue in the chain. The actual kinetics that are simulated using Monte Carlo techniques are compared with the results of analytical kinetic equations for the fraction of helix, (s), generated using the mean-field approximation. This mean-field rate equation is expanded as a hierarchy of terms that characterize the nature of rate constants for interacting systems. The first term in the expansion is first order in (s) and varies linearly with the interaction energy. Subsequent rate terms involve higher powers of (s) and demonstrate the need for nonlinear equations in systems with larger interaction energies. Both the simulations and the mean-field approximation show an intrinsic induction period for the single-step kinetic process. They also yield an apparent first-order rate constant that changes as the reaction proceeds. However, only the simulated kinetics yield ordered regions of chain and a nonzero, nearest-neighbor correlation function.

Thermodynamic treatment of nonphysical systems: Formalism and an example (Single-lane traffic)

An effort is made to introduce thermodynamic and statistical thermodynamic methods into the treatment of nonphysical (e.g., social, economic, etc.) systems. Emphasis is placed on the use of theentire thermodynamic framework, not merely entropy. Entropy arises naturally, related in a simple manner to other measurables, but does not occupy a primary position in the theory. However, the maximum entropy formalism is a convenient procedure for deriving the thermodynamic analog framework in which undetermined multipliers are thermodynamic-like variables which summarize the collective behavior of the system. We discuss the analysis of Levine and his coworkers showing that the maximum entropy formalism is the unique algorithm for achieving consistent inference of probabilities. The thermodynamic-like formalism for treating a single lane of vehicular traffic is developed and applied to traffic in which the interaction between cars is chosen to be a particular form of the “follow-the-leader” type. The equation of state of the traffic, the distributions of velocity and headway, and the various thermodynamic-like parameters, e.g., temperature (collective sensitivity), pressure, etc. are determined for an experimental example (Holland Tunnel). Nearest-neighbor and pair correlation functions for the vehicles are also determined. Many interesting and suggestive results are obtained,

Theory of domain growth in an order-disorder transition

We consider the growth of order in a two-dimensional Ising system with spin-flip dynamics (no conservation laws) quenched from above to below ${T}_{c}$. We use an iterative method, which allows for the interaction among many length and time scales, to calculate correlation functions in coordinate and Fourier space as a function of the time after quench. The method which we use to derive recursion relations is a reformulation of our previous work. We derive analytically scaling forms for the "Bragg peak" part of dynamic structure factor $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{C}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},t)$, the nearest-neighbor correlation function, the width of the central peak, ${q}_{w}$, and the maximum value of the peak. We evaluate the corresponding scaling functions. These scaling laws for the width and peak height are new and elucidate the role of the final temperature in the problem. In particular, we find that the peak height grows as ${t}^{\frac{7}{8}}$ for quenches to precisely ${T}_{c}$. Our results also show that the Cahn-Allen curvature-driven growth law, ${q}_{w}\ensuremath{\sim}{t}^{\frac{\ensuremath{-}1}{2}}$, is valid after relatively short times in this system. Our results agree quantitatively with Monte Carlo calculations in direct comparisons.