Energy Correlation Functions Research Articles

Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated annealing method

We grew graphene epitaxially on 6H-SiC(0001) substrate by the simulated annealing method. The mechanisms that govern the growth process were investigated by testing two empirical potentials, namely, the widely used Tersoff potential [J. Tersoff, Phys. Rev. B 39, 5566 (1989)] and its more refined version published years later by Erhart and Albe [Phys. Rev. B 71, 035211 (2005)]. Upon contrasting the results obtained by these two potentials, we found that the potential proposed by Erhart and Albe is generally more physical and realistic, since the annealing temperature at which the graphene structure just coming into view at approximately 1200 K is unambiguously predicted and close to the experimentally observed pit formation at 1298 K within which the graphene nucleates. We evaluated the reasonableness of our layers of graphene by calculating carbon-carbon (i) average bond-length, (ii) binding energy, and (iii) pair correlation function. Also, we compared with related experiments the various distance of separation parameters between the overlaid layers of graphene and substrate surface.

Novel Structures and Properties of Ni Nanowires

Atomic structures and properties of Ni nanowires are studied by using the generalized simulated annealing method with SuttonChen potential. Amorphous-like, helical, face-centered cubic and defect structures are found for different wire lengths. And from the analyses of the binding energy and angular correlation function (ACF), it is found that the helical structure of the Ni nanowires is the most stable form. With the compression and extension, the nanowires could transform from fcc [11 structure to fcc [110] one.

Energy correlation functions for jet substructure

Abstract We show how generalized energy correlation functions can be used as a powerful probe of jet substructure. These correlation functions are based on the energies and pair-wise angles of particles within a jet, with (N + 1)-point correlators sensitive to N-prong substructure. Unlike many previous jet substructure methods, these correlation functions do not require the explicit identification of subjet regions. In addition, the correlation functions are better probes of certain soft and collinear features that are masked by other methods. We present three Monte Carlo case studies to illustrate the utility of these observables: 2-point correlators for quark/gluon discrimination, 3-point correlators for boosted W /Z/Higgs boson identification, and 4-point correlators for boosted top quark identification. For quark/gluon discrimination, the 2-point correlator is particularly powerful, as can be understood via a next-to-leading logarithmic calculation. For boosted 2-prong resonances the benefit depends on the mass of the resonance.

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.

A comparison of the performance of Wang–Landau-Transition-Matrix algorithm with Wang–Landau algorithm for the determination of the joint density of states for continuous spin models

Monte Carlo simulation has been performed in a one-dimensional Lebwohl–Lasher model and two-dimensional XY-model using the Wang–Landau (WL) and the Wang–Landau-Transition-Matrix (WLTM) Monte Carlo methods. Random walk has been performed in the two-dimensional space comprising of energy-order parameter and energy-correlation function and the joint density of states (JDOS) were obtained. From the JDOS the order parameter, susceptibility and correlation function are calculated. Agreement between the results obtained from the two algorithms is very good. The work shows that for the purpose of determination of JDOS, the WLTM method is a good alternative to the WL algorithm.

Molecular Dynamics Simulation of Interactions on Graphene/Polypyrrole Nanocomposites Interface

Graphene receives world-wide attention due to its unique two-dimensional structure and exceptional electrical and mechanical properties. The graphene/polypyrrole (Gr/PPy) nanocomposites, have been synthesized via dispersing the graphene into polymers, which can be widely used in microwave absorption, supercapacitors and electronic devices. Molecular dynamics simulations are carried out to investigate the microscopic mechanism of interactions on Gr/PPy nanocomposites interface. The interaction configurations, intermolecular interaction energy and pair correlation functions between graphene and PPy are computed. The curves of temperature, energy evolution and interaction energy analysis indicate that Gr/PPy system reaches equilibrium in a relatively short time, and it is a thermodynamic equilibrium system. The interaction configurations show that there is an attractive interaction between the graphene and PPy. Pair correlation functions reveal that there are van der Waals interactions and hydrogen bond between the graphene and PPy, which are strong short-range non-bonded interactions. The strong interactions mainly arise from the sp2 hybridized π-conjugated structure of graphene and PPy, which engenders π-π interaction.

Energy spectrum and correlation functions of clusters of carbon nanotubes with the (5, 5) chirality

The correlation functions and energy spectra of clusters of carbon nanotubes with the (5, 5) chirality that consist of 30, 50, 70, 90, and 190 atoms have been obtained in terms of the Hubbard model. It has been assumed that, taking into account the Hubbard correlations, carbon nanotubes with the (5, 5) chirality should be semiconductors with a band gap of ∼1 eV. This contradicts the generally accepted concept, according to which carbon nanotubes with the (m, n) chirality should be metals if the difference in the chirality indices m − n is multiple to three or equal to zero. The results obtained have been compared with experimental data on electrical conductivity and scanning tunneling microscopy of carbon nanotubes.

Discrete symmetry breaking transitions between paired superfluids

We explore the zero-temperature phase diagram of bosons interacting via Feshbach resonant pairing interactions in one dimension. Using DMRG (Density Matrix Renormalization Group) and field theory techniques we characterize the phases and quantum phase transitions in this low-dimensional setting. We provide a broad range of evidence in support of an Ising quantum phase transition separating distinct paired superfluids, including results for the energy gaps, correlation functions and entanglement entropy. In particular, we show that the Ising correlation length, order parameter and critical properties are directly accessible from a ratio of the atomic and molecular two-point functions. We further demonstrate that both the zero-momentum occupation numbers and the visibility are in accordance with the absence of a purely atomic superfluid phase. We comment on the connection to recent studies of boson pairing in a generalized classical XY model.

Charged magnetic brane correlators and twisted Virasoro algebras

Prior work using gauge/gravity duality has established the existence of a quantum critical point in the phase diagram of 3+1-dimensional gauge theories at finite charge density and background magnetic field. The critical theory, obtained by tuning the dimensionless charge density to magnetic field ratio, exhibits nontrivial scaling in its thermodynamic properties, and an associated nontrivial dynamical critical exponent. In the present work, we analytically compute low energy correlation functions in the background of the charged magnetic brane solution to 4+1-dimensional Einstein-Maxwell-Chern-Simons theory, which represents the bulk description of the critical point. Results are obtained for neutral scalar operators, the stress tensor, and the U(1)-current. The theory is found to exhibit a twisted Virasoro algebra, constructed from a linear combination of the original stress tensor and chiral U(1)-current. The effective speed of light in the IR is renormalized downward for one chirality, but not the other, by finite density, a behavior that is consistent with a Luttinger liquid description of fermions in the lowest Landau level. The results obtained here do not directly shed light on the mechanism driving the phase transition, and we comment on why this is so.

Continuous-time Monte Carlo methods for quantum impurity models

Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. We present derivations and descriptions of the algorithms in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied and outline prospects for future applications.

Power-law behavior of bond energy correlators in a Kitaev-type model with a stable parton Fermi surface

We study bond energy correlation functions in an exactly solvable quantum spin model of Kitaev type on the kagome lattice with stable Fermi surface of partons proposed recently by Chua et al, Ref.\[arXiv:1010.1035]. Even though any spin correlations are ultra-short ranged, we find that the bond energy correlations have power law behavior with a $1/|{\bm r}|^3$ envelope and oscillations at incommensurate wavevectors. We determine the corresponding singular surfaces in momentum space, which provide a gauge-invariant characterization of this gapless spin liquid.

Studies of Liquid–Solid Transitions Using a Thermodynamic Perturbation Method with Modified Weighted Density Approximation

Despite intensive investigations based on statistical mechanics, liquid–solid transition is far from complete understanding. The reason for this difficulty lies in the fact that any conventional theory including the density functional theory cannot handle the attractive part that exists in any interaction potential. Thus far, a density functional theory incorporated with the modified weighted density approximation (MWDA) has been developed to predict the liquid–solid transition of a hard-sphere system. In this approach, the free energy and direct correlation function (DCF) in a liquid state were calculated using the analytical solution of the Percus–Yevick (PY) equation. The coexisting density of solid and liquid states given by this approach has agreed with those obtained by computer simulations within 0.7%. However, this method cannot be applied to realistic systems where constituents interact mutually through potential energy with an attractive part. This is because there are no analytical expressions available for the free energy and DCF. In this short note, we apply an alternative approach to analyzing liquid–solid transitions for atoms whose interaction potential has an attractive part. We employ a thermodynamic perturbation method developed by Rascon et al. The method has been applied successfully to the analysis of systems with nonmonotonic potential energy such as the Lennard-Jones, square well, and Dzugutov potential. The required information in this approach is only the potential function and the structure of a solid. Exploiting the theory developed by Weeks, Chandler, and Andersen (WCA), we first expand the free energy of the liquid and solid states. Namely, we split the potential energy into a hard-sphere reference potential and a perturbation potential. Thus, the free energy can be written as F1⁄2 ðrÞ 1⁄4 FHS1⁄2 ðrÞ þ 2 N 2 V Z 1

Search for electron liquids with non-Abelian quasiparticles

We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors 7/3 < ve < 8/3. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at ve = 5/2 (paired Moore–Read "pfafian" state) and 12/5 (clustered Read–Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline ve = 7/3 state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.

Exploration of Parameters of Ashcroft’s Potential Using Monovacancy Formation Energy and Different Exchange and Correlation Functions for some Trivalent FCC Metals

A pseudopotential approach has been used to study the variation of the vacancy formation energy as a function of the parameter of Ashcroft's empty core model potential (AECMP) and nine different exchange and correlation functions (ECF) for some trivalent fcc metals, viz. Al, La, Sc, γ-Ce, Pr and Yb. The criterion used is that should be greater than the Bohr radius ( ). There is a systematic increase in the fitted value of in going from one ECF to another, as follows: KK &lt; Sham &lt; GV &lt; Kle &lt; Harr &lt; VS &lt; Tay &lt; Hub &lt; MD and it is difficult to assign a particular value of for all ECFs for a particular trivalent fcc metal. The inherent simplicity of AECMP makes it difficult to have a universal parameter for all types of atomic property calculations.

Transition from Abelian to non-Abelian quantum liquids in the second Landau level

The search for non-Abelian quantum Hall states in the second Landau level is narrowed to the range of filling factors 7/3<\nu_e<8/3. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at \nu_e=5/2 (Moore--Read) and 12/5 (Read--Rezayi). Outside of it, the four-flux noninteracting composite fermion model is validated. The borderline \nu_e=7/3 state is adiabatically connected to the Laughlin liquid, but its short-range correlations and charge excitations are different.

Mechanisms for Thermal Conduction in Methane Hydrate

Crystalline clathrate hydrates exhibit an unusual thermal transport with glasslike thermal conductivity close to the Debye temperature but a crystal-like temperature dependence at low temperature. Molecular dynamics calculations on structure I methane clathrate hydrate reproduced the qualitative trend in the thermal conductivity. Analysis of the heat flux and local energy correlation functions shows that both the crystal structure of the clathrate framework and guest-host interactions contribute to thermal transport processes. The lower thermal conductivity relative to ice Ih is due to differences in crystal structures. The glasslike temperature dependence is governed by the guests and the guest-host interactions.

Measures on two-component configuration spaces

We study the measures on the congur ation spaces of particles of two types. Gibbs measures on such spaces are described. Main properties of corresponding relative energy densities and correlation functions are considered. In particular, we show that a support set for such Gibbs measure is the set of pairs of non-intersected congur ations.

Relatinge+e−annihilation to high energy scattering at weak and strong coupling

We explore the correspondence between the final state in e^+e^- annihilation and the small-x hadronic wavefunction in the transverse plane both in weakly coupled QCD and strongly coupled N=4 SYM. At strong coupling, the virtual and static photon produced in e^+e^- annihilation can be treated as a shock wave propagating in AdS space leaving spherical energy and charge distributions on the boundary. This is shown to be mathematically identical to the computation of energy and charge distributions in the transverse plane generated by a high energy color singlet state. At weak coupling, the correspondence is useful in studying interjet observables. By performing the stereographic projection to the BFKL equation, we construct an exact solution to the evolution equation derived by Marchesini and Mueller, and find the angular distribution of small-x gluons in the interjet region. Finally we argue that the correspondence holds also for the energy correlation functions.

Excitation energy and pair correlation function of trions near an LiF surface

We investigate the excitation spectrum of a singly charged LiF surface using an embedded cluster approach. The spectrum is determined by multiconfiguration self-consistent field calculations. We find stable trionic states, i.e., quasimolecular states of a three-quasiparticle complex consisting of two holes and one electron interacting through the Coulomb potential. The excitation energy of the lowest trionic state is approximately 12.1 eV. The mean hole-hole spacing is about 7.6 a.u. (or $4\text{ }\text{\AA{}}$). Our results confirm the interpretation of experiments [P. Roncin et al., Phys. Rev. Lett. 89, 043201 (2002)] where trion excitation was suggested as effective energy-loss channel during the neutralization of ${\text{Ne}}^{+}$ ions at an LiF surface.