Nonlocal Correlation Functions Research Articles

Exotic phase diagram of a topological quantum system

We study the quantum phase transitions (QPTs) in the Kitaev spin model on a triangle-honeycomb lattice. In addition to the ordinary topological QPTs between Abelian and non-Abelian phases, we find new QPTs which can occur between two phases belonging to the same topological class, namely, either two non-Abelian phases with the same Chern number or two Abelian phases with the same Chern number. Such QPTs result from the singular behaviors of the nonlocal spin-spin correlation functions at the critical points.

Non-equilibrium relaxation and near-arrest dynamics in colloidal suspensions

In this work we propose a theory to describe the irreversible diffusive relaxation of the localconcentration of a colloidal dispersion that proceeds toward its stable thermodynamicequilibrium state, but which may in the process be trapped in metastable or dynamicallyarrested states. The central assumption of this theory is that the irreversiblerelaxation of the macroscopically observed mean value of the local concentration of colloidal particles is described by a diffusion equation involving a localmobility b*(r,t) that depends not only on the mean value but also on the covariance of the fluctuations . This diffusion equation must hence be solved simultaneously with the relaxation equation for thecovariance σ(r,r′;t), and here we also derive the corresponding relaxation equation. The dependence of the local mobilityb*(r,t) on the mean value and the covariance is determined by a self-consistent set of equationsinvolving now the spatially and temporally non-local time-dependent correlation functions,which in a uniform system in equilibrium reduces to the self-consistent generalizedLangevin equation (SCGLE) theory of colloid dynamics. The resulting general theoryconsiders the possibility that these relaxation processes occur under the influence ofexternal fields, such as gravitational forces acting in the process of sedimentation. In thispaper, however, we describe a simpler application, in which the system remainsspatially uniform during the irreversible relaxation process, and discuss the generalfeatures of the glass transition scenario predicted by this non-equilibrium theory.

Identifying Phases of Quantum Many-Body Systems That Are Universal for Quantum Computation

Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state model, and by using nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits, we demonstrate that it possesses a quantum (zero-temperature) phase transition between a disordered phase and an ordered "cluster phase" in which it is possible to perform a universal set of quantum gates.

Symplectic tomography of ultracold gases in tight waveguides

The phase space is the natural ground to smoothly extrapolate between local and nonlocal correlation functions. With this objective, we introduce the symplectic tomography of many-body quantum gases in tight waveguides, and concentrate on the reduced single-particle symplectic tomogram (RSPST) whose marginals are the density profile and momentum distribution. We present an operational approach to measure the RSPST from the time evolution of the density profile after shutting off the interactions in a variety of relevant situations: Free expansion, fall under gravity, and oscillations in a harmonic trap. From the RSPST, the one-body density matrix of the trapped state can be reconstructed.

Spatial Nonlocal Pair Correlations in a Repulsive 1D Bose Gas

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.

Equations-of-motion approach to the spin-12Ising model on the Bethe lattice

We exactly solve the ferromagnetic spin- 1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is applied to an isomorphic model of localized Fermi particles interacting via an intersite Coulomb interaction. A complete set of eigenoperators is found together with the corresponding eigenvalues. The Green's functions and the correlation functions are written in terms of a finite set of parameters to be self-consistently determined. A procedure is developed that allows us to exactly fix the unknown parameters in the case of a Bethe lattice with any coordination number z. Nonlocal correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities.

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

An improved epsilon expansion in the d -dimensional (d > 2) stochastic theory of turbulence is constructed at two-loop order, which incorporates the effect of pole singularities at d--> 2 in coefficients of the epsilon expansion of universal quantities. For a proper account of the effect of these singularities, two different approaches to the renormalization of the powerlike correlation function of the random force are analyzed near two dimensions. By direct calculation, it is shown that the approach based on the mere renormalization of the nonlocal correlation function leads to contradictions at two-loop order. On the other hand, a two-loop calculation in the renormalization scheme with the addition to the force correlation function of a local term to be renormalized instead of the nonlocal one yields consistent results in accordance with the ultraviolet (UV) renormalization theory. The latter renormalization prescription is used for the two-loop renormalization-group analysis amended with partial resummation of the pole singularities near two dimensions, leading to a significant improvement of the agreement with experimental results for the Kolmogorov constant.

Nonlocal effects in the electron-positron interaction in metals

We study the importance of the nonlocal electron-positron interaction for positron annihilation characteristics in simple and transition metals. This is accomplished by using the weighted density approximation, giving rise to nonlocal and energy-dependent electron-positron correlation functions. We apply this formalism to study the momentum-dependent and momentum-averaged electron-positron enhancements of the positron annihilation rates and the three-dimensional electron-positron momentum densities. The results of the present approach are compared to those obtained within the local density approximation, generalized gradient approximation, Bloch modified ladder approximation, and experimental data. We find that while nonlocality of the electron-positron correlations is of substantial importance for the core and d electrons in transition metals, for nearly-free-electron bands the energy dependence of the electron-positron correlation functions is of more significance.

Critical behavior in systems with a long-range correlated frozen-in random field

The critical behavior of inhomogeneous systems with a frozen-in random field having a nonlocal correlation function decaying according to the power law $|\mathbf{x}\ensuremath{-}{\mathbf{x}}^{\ensuremath{'}}{|}^{\ensuremath{-}b}$ is considered. The problem is studied within the context of a model which partially considers interactions of fluctuations and belongs in the same universality class as the spherical model. Depending on the relationship between the power b and the space dimensionality d, a new critical behavior arises.

Interacting electrons with spin in a one-dimensional dirty wire connected to leads

We investigate a one--dimensional wire of interacting electrons connected to one--dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of an incident electron even in the noninteracting leads. The Fourier transform of nonlocal correlation functions are computed for $T\gg \omega$. In particular, this allows us to study the proximity effect, related to the Andreev reflection. A new type of proximity effect emerges when the wire has normally a tendency towards Wigner crystal formation. The latter is suppressed by the leads below a space--dependent crossover temperature; it gets dominated everywhere by the $2k_F$ CDW at $T<L^{3/2 (K-1)}$ for short range interactions with parameter $K<1/3$. The lowest--order renormalization equations of a weak backscattering potential are derived explicitly at finite temperature. A perturbative expression for the conductance in the presence of a potential with arbitrary spatial extension is given. It depends on the interactions, but is also affected by the noninteracting leads, especially for very repulsive interactions, $K<1/3$. This leads to various regimes, depending on temperature and on $K$. For randomly distributed weak impurities, we compute the conductance fluctuations, equal to that of $R=g-2e^2 /h$. While the behavior of $Var(R)$ depends on the interaction parameters, and is different for electrons with or without spin, and for $K<1/3$ or $K>1/3$, the ratio $Var(R)/R^2$ stays always of the same order: it is equal to $L_T/L\ll 1$ in the high temperature limit, then saturates at 1/2 in the low temperature limit, indicating that the relative fluctuations of $R$ increase as one lowers the temperature.

Nonlocal electron-positron correlations in solids within the weighted density approximation

Nonlocal electron-positron correlation effects in solids are studied. The weighted density approximation (WDA) is applied to calculations of the nonlocal state-selective electron-positron correlation functions. The importance of state selectivity of the electron-positron enhancement factors is discussed. The calculated WDA electron-positron enhancement factors for the core electrons are compared with those obtained within the local-density approximation. Also, differences in the electron-positron enhancement factors due to the $s,$ $p,$ $d,$ and $f$ angular momentum channels of the electron charge density are studied. The influence of the electron-positron interaction on the positron density distribution in solids is discussed. The formalism is applied to ab initio calculations of positron lifetimes in a variety of metals and silicon. The influence of various approximations to the electron-positron interaction on the positron lifetimes is also presented. Moreover, we study how the core electrons as well as different angular momentum channels of the valence electron density contribute to the total positron annihilation rates and lifetimes. The results are compared to those calculated within the local-density approximation and the generalized gradient approximation.

S=2 antiferromagnetic quantum spin chain.

We have investigated Haldane's conjecture for the S=2 antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite gap of \ensuremath{\Delta}=0.085(5)J and a finite spin-spin correlation length \ensuremath{\xi}=49(1) lattice spacings. We have confirmed the gap value by a zero-temperature quantum Monte Carlo study. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function which saturates to a nonzero value in the thermodynamic limit. We investigate the behavior of the spin-2 chain under an easy-plane anisotropy D(${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$${)}^{2}$, D\ensuremath{\gtrsim}0, and find that the Haldane and the large-D phase are separated by an XY phase. The string correlation function vanishes only in the D\ensuremath{\rightarrow}\ensuremath{\infty} limit and does not distinguish between the Haldane phase and the perturbative large-D phase. An analysis of the transition mechanism and of the S=2 phase diagram in the presence of easy-plane and exchange anisotropy, markedly different from the S=1 phase diagram, allow us to conjecture how the classical limit is reached from increasing integer spins. \textcopyright{} 1996 The American Physical Society.

Mechanism of Atmospheric Photooxidation of Aromatics: A Theoretical Study

The mechanisms of atmospheric photooxidation of aromatic compounds are of seminal importance in the chemistry of the urban and regional atmosphere. It has been difficult to experimentally account for the full spectrum of oxidation products in laboratory studies. In an effort to fully elucidate the atmospheric reaction pathways for the aromatic−OH reaction, we have conducted theoretical calculations on aromatic intermediates. Energies have been determined for these intermediates by using semiempirical UHF/PM3 geometry optimizations combined with ab initio calculations using density functional theory (DFT). A hybrid DFT model, the Becke3 parameter function with the nonlocal correlation function of Lee, Yang, and Parr, was used in conjunction with the 6-31G(d,p) basis set to study the intermediate structures. Full mechanisms for the OH-initiated photooxidation of toluene, m-xylene, p-xylene, 1,2,4-trimethylbenzene, and m-ethyltoluene are developed. The lowest energy intermediates have been determined, and predicted products from these structures are compared to available experimental product data. These studies serve to refine proposed mechanisms currently available for toluene, m-xylene, and p-xylene, while providing new information on the 1,2,4-trimethylbenzene and m-ethyltoluene reaction pathways.

Mean‐Field Solution of Strongly Correlated Systems Using Hubbard Atomic Operators. Hubbard Model with Infinite U

AbstractThe hierarchy of equations of motion for double‐time Green functions for Hubbard atomic operators is solved using moment‐conserving decoupling. The lowest order gives a new type of meanfield solution which depends on nonlocal correlation functions. The case of Hubbard model with infinite Coulomb interaction is studied and magnetic properties of the mean‐field solution are investigated employing an additional approximation for correlation functions.

Nonradiative lifetime of excited states near a small metal particle.

The nonradiative lifetime of excited states near a small (\ensuremath{\lesssim}2 nm) metal particle is investigated within a purely electromagnetic model. The excited state is described as a point dipole, and the metal particle is characterized by its self-consistently obtained nonlocal density-density correlation function. Resonant coupling, between excited states of adsorbates and various electronic excitations of the metal particle, is shown to be an important lifetime-determining decay channel.

The nonlocal correlation functionG(1,2) in density functional theory

We have analyzed the nonlocal contribution A(1) = ∇1 · ∇2G(1,2)|2→1 to the kinetic energy density term for a few representative atomic systems in order to gain some insight into the factors which are responsible for the occurrence of shell structure. We have advanced a method for obtaining the nonlocal correlation function G(1,2) once A(1) is known. We discuss simple analytic approximations to A(1) and hence to G(1,2) which could be used for the construction of an energy density functional based on ρ.

Exact computation of loop averages in two-dimensional Yang-Mills theory

We present an explicit algorithm that allows the exact computation of all nonlocal gauge-invariant correlation functions in two-dimensional Yang-Mills theory. Explicit expressions are given for the expectation value of entangled loop operators and their products in the $\mathrm{U}(N)$ theory with arbitrary $N$.Using these results we show that the Schwinger-Dyson equation for loops holds without singularities in the continuum, and we verify the factorizability of the correlation functions in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. A non-Abelian version of Stokes's theorem which is used in the calculations is derived for an arbitrary number of dimensions.