Pair-pair Correlation Function Research Articles

Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-T c Superconductivity in La3Ni2O7 under High Pressure

High-T c superconductivity with possible T c ≈ 80 K has been reported in the single crystal of La3Ni2O7 under high pressure. Based on the electronic structure given by the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both 3d z 2 and 3d x 2–y 2 orbital electrons of the nickel cations. The main feature of the model is that the 3d z 2 electrons form inter-layer σ-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the 3d x 2–y 2 electrons hybridize with the 3d z 2 electrons within each NiO2 plane. The chemical potential difference of these two orbital electrons ensures that the 3d z 2 orbitals are close to half-filling and the 3d x 2–y 2 orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the 3d z 2 orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange J. Applying pressure can self dope holes on the 3d z 2 orbitals with the same amount of electrons doped on the 3d x 2–y 2 orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large J and small doping of 3d z 2 orbitals, we find the superconducting instability on both the 3d z 2 and 3d x 2–y 2 orbitals by calculating the equal-time spin singlet pair–pair correlation function. Our numerical results may provide useful insights in the high-T c superconductivity in single crystal La3Ni2O7 under high pressure.

Superconducting properties of the hole-doped three-band d−p model studied with minimal-size real-space d -wave pairing operators

The three-band \emph{d-p} model is investigated by means of Variational Monte-Carlo (VMC) method with the BCS-like wave-function supplemented by the Gutzwiller and Jastrow correlators. The VMC optimization leads to $d$-$wave$ superconducting state with a characteristic dome-like shape of the order parameter for hole doping $\delta \lesssim 0.4$, in a good agreement with the experimental observations. Also, the off-diagonal pair-pair correlation functions, calculated within VMC, vindicates the results obtained very recently within the diagrammatic expansion of the Gutzwiller wave function method (DE-GWF) [cf. Phys. Rev. B \textbf{99}, 104511 (2019)]. Subsequently, the nature of the $d$-$wave$ pairing is investigated by means of recently proposed \emph{minimal-size real-space d-wave pairing operators} [Phys. Rev. B \textbf{100}, 214502 (2019)]. An emergence of the long-range superconducting ordering for both $d$ and $p$ orbitals is reported by analysing the corresponding off-diagonal pair-pair correlation functions. The dominant character of \emph{d-wave} pairing on $d$ orbitals is confirmed. Additionally, the trial wave-function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out and shows antiferromagnetic $\mathbf{q}=(\pi,\pi)$, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value $\Delta_{CG}\approx1.78\pm0.51\text{ eV}$, and agrees with values reported experimentally for the cuprates.

Principal component analysis for fermionic critical points

We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine $T_c$. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

Modulation of pairing symmetry with bond disorder in unconventional superconductors

We study a two-orbital $t$-$J_1$-$J_2$ model, originally developed to describe iron-based superconductors at low energies, in the presence of bond disorder (via next-nearest-neighbor $J_2$-bond dilution). By using the Bogoliubov--de Gennes approach, we self-consistently calculate the local pairing amplitudes and the corresponding density of states, which demonstrate a change of dominant pairing symmetry from $s_\pm$ wave to $d$ wave when increasing disorder strength as long as $J_1\lesssim J_2$. Moreover, the combined pairing interaction and strong bond disorder lead to the formation of $s_\pm$ wave "islands" with length scale of the superconducting coherence length embedded in a $d$ wave "sea." This picture is further complemented by the disorder-averaged pair-pair correlation functions, distinct from the case with potential disorder, where the "sea" is insulating. Due to this inevitable formation of spatial inhomogeneity, the superconducting $T_c$ determined by the superfluid density $\rho_s(T)$ obviously deviates from the value predicted by the conventional Abrikosov-Gorkov theory, where the pairing amplitudes are viewed as uniformly suppressed as the disorder increases.

Order parameter, correlation functions, and fidelity susceptibility for the BCS model in the thermodynamic limit

The exact ground state of the reduced BCS Hamiltonian is investigated numerically for large system sizes and compared with the BCS ansatz. A ``canonical'' order parameter is found to be equal to the largest eigenvalue of Yang's reduced density matrix in the thermodynamic limit. Moreover, the limiting values of the exact analysis agree with those obtained for the BCS ground state. Exact results for the ground-state energy, level occupations, and a pseudospin-pseudospin correlation function are also found to converge to the BCS values already for relatively small system sizes. However, discrepancies persist for a pair-pair correlation function, for interlevel correlations of occupancies and for the fidelity susceptibility, even for large system sizes where these quantities have visibly converged to well-defined limits. Our results indicate that there exist nonperturbative corrections to the BCS predictions in the thermodynamic limit.

Hydration of Zwitterionic Glycine Betaine and Analogues Through Molecular Simulation

We use molecular dynamics simulation to characterize the hydration of 3 molecules important to protein stability: zwitterionic glycine, zwitterionic N,N-dimethylglycine, N,N,N-trimethylglycine (glycine betaine). Both structuring and dynamics of bulk and bound water were examined using a variety of properties and at multiple concentrations. Metrics such as radial distribution functions and residence times were used to characterize hydration. Also, we used more specialized metrics that can discriminate between subtle differences in hydration such as condensed phase order parameters, Voronoi tessellations, and multidimensional pair-pair correlation functions. Trimethylglycine was found to have a unique hydration shell that extends across the entire molecule and has no specific interactions between solute molecules. Glycine was found to aggregate and have a more disjoint hydration shell. Lastly, trimethylglycine is disperse in solution even at very high concentrations and water rapidly moves between trimethylglycine amine groups. The differences in hydration structure between the three zwitterions can be seen in Figure 1, which shows the radial distribution function between the amine and waters. This work has meaningful implications for protein stability where trimethylglycine is known to prevent protein aggregation and interfaces where trimethylglycine prevents protein adsorption.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Polyunsaturated and Saturated Phospholipids in Mixed Bilayers: A Study from the Molecular Scale to the Lateral Lipid Organization

Polyunsaturated lipids are remarkably flexible molecules, with a great influence on the membrane structure and dynamics, affecting from mechanical properties to domain segregation. In this work, we studied phospholipid mixtures of dipalmitoylphosphatidylcholine (DPPC) and diunsaturated phosphatidylcholine lipids (diunsPC) of different lengths, by means of molecular dynamic simulations of a coarse-grained interaction model. These diunsPC:DPPC binary mixtures show nonideal behavior characterized by one mixed phase with composition fluctuations on a length scale of nanometers. Motivated by this observation, we studied comprehensively the characteristics of molecular structure as a function of the compositional gradient. We analyzed orientational order profiles, density distributions, and pair-pair correlation functions between the molecule residues. We observed that, in diunsPC-enriched regions, DPPC tails become expanded and disordered, especially toward the membrane center. On the other hand, in the more condensed DPPC-enriched patches, diunsaturated acyl chains become displaced toward the interface instead of stretching along the membrane normal. From the comparison of the two diunsPC lipids of different tail length, we measured that the presence of a longer terminal saturated segment induces better mixing with DPPC, and most interestingly eliminates the up-down composition correlation measured with the shorter tail-diunsPC. At molecular level, there is a reduced redistribution of densities and changes in the local order as a function of composition. We interpret these results as indicative that the packing incompatibility between polyunsaturated and saturated lipids rules their mixing behavior.

Local and Bulk Hydration of Zwitterionic Glycine and its Analogues through Molecular Simulations

Molecular dynamics simulations were used to characterize the differences in hydration between glycine and two of its zwitterionic analogues: N,N-dimethylglycine and N,N,N-trimethylglycine (glycine betaine). The hydration of dodecane and oligo(ethylene glycol) was studied for reference. Both structuring and dynamics of bulk and bound water were examined using a variety of properties and at multiple concentrations. Metrics, such as radial distribution functions and residence times, were used to characterize hydration. Also, we used more specialized metrics that can discriminate between subtle differences in hydration, such as condensed phase order parameters, Voronoi tessellations, and multidimensional pair-pair correlation functions. Trimethylglycine was found to have a unique hydration shell that extends across the entire molecule and has no specific interactions between solute molecules. Also, we found that dimethylglycine has a similar hydration structure to that of trimethylglycine despite its hydrogen-bond donor. Glycine was found to aggregate and have a more disjoint hydration shell. All three zwitterions were found to structurally affect water within 1.5-2.0 coordination shells. Lastly, trimethylglycine is disperse in solution even at very high concentrations, and water rapidly moves between trimethylglycine amine groups. This work has meaningful implications for protein stability where trimethylglycine is known to prevent protein aggregation and nonfouling interfaces where trimethylglycine prevents nonspecific protein adsorption.

Lattice calculation of thermal properties of low-density neutron matter with pionlessNNeffective field theory

Thermal properties of low-density neutron matter are investigated by determinantal quantum Monte Carlo lattice calculations on 3+1 dimensional cubic lattices. Nuclear effective field theory (EFT) is applied using the pionless single- and two-parameter neutron-neutron interactions, determined from the ${}^{1}{S}_{0}$ scattering length and effective range. The determination of the interactions and the calculations of neutron matter are carried out consistently by applying EFT power counting rules. The thermodynamic limit is taken by the method of finite-size scaling, and the continuum limit is examined in the vanishing lattice filling limit. The ${}^{1}{S}_{0}$ pairing gap at $T\ensuremath{\approx}0$ is computed directly from the off-diagonal long-range order of the spin pair-pair correlation function and is found to be approximately 30% smaller than BCS calculations with the conventional nucleon-nucleon potentials. The critical temperature ${T}_{c}$ of the normal-to-superfluid phase transition and the pairing temperature scale ${T}^{*}$ are determined, and the temperature-density phase diagram is constructed. The physics of low-density neutron matter is clearly identified as being a BCS-Bose-Einstein condensation crossover.

Exact Numerical Study of Pair Formation with Imbalanced Fermion Populations

We present an exact quantum Monte Carlo study of the attractive one-dimensional Hubbard model with imbalanced fermion population. The pair-pair correlation function, which decays monotonically in the absence of polarization P, develops oscillations when P is nonzero, characteristic of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. The pair momentum distribution peaks at a momentum equal to the difference in the Fermi momenta. At strong coupling, the minority and majority momentum distributions are shown to be deformed, reflecting the presence of the other species and its Fermi surface. The FFLO oscillations survive the presence of a confining potential, and the local polarization at the trap center exhibits a marked dip, similar to that observed experimentally.

Magnetism and superconductivity in thet−t′−Jmodel

We present a systematic study of the phase diagram of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model by using the Green's function Monte Carlo (GFMC) technique, implemented within the fixed-node (FN) approximation and a wave function that contains both antiferromagnetism and $d$-wave pairing. This enables us to study the interplay between these two kinds of order and compare the GFMC results with the ones obtained by the simple variational approach. By using a generalization of the forward-walking technique, we are able to calculate true FN ground-state expectation values of the pair-pair correlation functions. In the case of ${t}^{\ensuremath{'}}=0$, there is a large region with a coexistence of superconductivity and antiferromagnetism that survives up to ${\ensuremath{\delta}}_{c}\ensuremath{\sim}0.10$ for $J∕t=0.2$, and ${\ensuremath{\delta}}_{c}\ensuremath{\sim}0.13$ for $J∕t=0.4$. The presence of a finite ${t}^{\ensuremath{'}}∕tl0$ induces a strong suppression of both magnetic (with ${\ensuremath{\delta}}_{c}\ensuremath{\lesssim}0.03$ for $J∕t=0.2$ and ${t}^{\ensuremath{'}}∕t=\ensuremath{-}0.2$) and pairing correlations. In particular, the latter ones are depressed both in the low-doping regime and around $\ensuremath{\delta}\ensuremath{\sim}0.25$, where strong size effects are present.

Medium-Range Order Structures of Amorphous Diamond-Like Carbon Films

ABSTRACTIn this paper, we have studied medium-range order structures in amorphous diamond-like carbon films with fluctuation microscopy. Medium-range order structures are quantified by a specific form of a general four-body correlation. We name this function as a pair-pair alignment correlation function. By analyzing speckle dark-field images taken over different areas as a function of momentum transfer in reciprocal space, we measured the pair-pair alignment correlation function for both thermally annealed samples and unannealed samples. We have found that thermal annealing introduces medium-range order in amorphous diamond-like carbon films, causing more pairs of atoms to be aligned. These results agree with density-functional simulations. Larger-scale simulations will be needed to fully understand our experimental results.

Pairing correlation of t-J type models studied by the power-Lanczos method

We reported that the pair-pair correlation function of the two-dimensional t- J model has very small long-range d-wave superconducting correlation in the physical parameter range of J/ t ≤ 0.5. The power-Lanczos method is used under the assumption of monotonic behavior, which has been well checked in the two-dimensional t-J and attractive Hubbard models. Here we examine this criterion for the t-J model in two-leg ladders. The exponent of the power law decay of the pairing correlation behaves monotonically up to 12 powers and is in good agreement with the DMRG and exact results. The criterion is applied to the two-dimensional t - t′ - J model. The results show that negative t′/ t suppresses the pairing correlation further, and we conclude that the long-range pairing correlation in the t - t′ - J model with t′/ t < 0 is also seemingly too small to account for the high temperature superconductivity.

D-Wave Pairing Correlation in the Two-Dimensionalt−JModel

The pair-pair correlation function of the two-dimensional t-J model is studied by using the power-Lanczos method and an assumption of monotonic behavior. In comparison with the results of the ideal Fermi gas, we conclude that the 2D t-J model does not have long range d-wave superconducting correlation in the interesting parameter range of $J/t \leq 0.5$. Implications of this result will also be discussed.

A New Structural Study for an Old Quasicrystal

In this paper, we have described the experimental evidence for the polyhedral order in metastable Al-Mn alloy (icosahedral phase). We have used the anomalous diffractometry technique to identify the X-ray patterns of this alloy. For the first time, the radial distribution function of the diffuse rings scattered by this alloy is obtained by applying this new technique. Unlike previous methods used for interpreting the X-ray patterns of this phase, we have introduced a new method of separation for interpreting X-ray patterns. The X-ray diffraction pattern has been numerically resolved into a broad diffuse halo and sharp lines. Using this procedure the correlation position was deduced from a high quality interference function. We have not been able to explain either the origin of the sharp lines or the relationship of the two parts responsible for the lines and rings. In order to explain the above we need an appropriate geometrical model and some structural information on the medium range order of the atoms causing scattered rings. This information is contained in the partial pair-pair correlation function of the coherent background. The result of this work may be of aid in order to comprehend the genetic relationship between the structure of the crystalline, amorphous FK phases and this new metastable alloy or icosahedral phase.

THE STELLAR ANGULAR CORRELATION: CLUES TO WIDE BINARY STAR PROPERTIES

ABSTRACT The angular distribution of stars brighter than visual magnitude 14 is analyzed for evidence of gravitationally bound systems with widely separated components. Binary stars with separations on the order of 0.1 parsec are interesting as probes of Galactic dynamics, disk dark matter, the Oort comet cloud, and the postulated solar companion star, Nemesis. Catalogs of stars, complete to a resolution limit of four arcseconds, were constructed from digitized Schmidt telescope plates covering over 600 square degrees of the sky in four directions. I analyze the clustering properties of stars and star pairs using two-point and three-point angular correlation functions. Significant correlation (assumed to be due to binary stars) is detected only for angular separations less than 40 arcseconds. No significant numbers of ternary systems are detected. Employing a modified Wasserman-Weinberg technique, I directly compare the angular correlation functions with a simple model of wide binary star properties. The wide binary semimajor axis distribution at low Galactic latitudes is best described as a single power law of index -1.3. Near the North Galactic Pole (NGP), the power law is less steep and the distribution is consistent with a cutoff near 0.1~parsec. The derived wide binary density is unrealistically large, suggesting that the basic model inadequately characterizes wide binary properties. I also study a sample of stars from the Space Telescope Guide Star Catalog (GSC). The region analyzed lies within thirty degrees of the NGP and covers 2500 square degrees of sky. This large, low-resolution sample complements the smaller, more uniform plate catalogs. I identify many systematic errors in the GSC and attempt to account for image misclassifications and poorly defined resolution limits. The corrected stellar correlation function from the GSC is found to be consistent with a wide binary separation cutoff near 0.1parsec. The dissolution of a poor Galactic cluster at the NGP may explain the observed wide binary distribution in that direction. Evidence for weak clustering on scales of one degree is seen in the pair-pair correlation function. The unphysically large wide binary density derived from magnitude-limited samples is explained well by a luminosity correlation between the binary components. An alternative solution requires all F to K dwarfs to be members of wide binaries. Based on the observed properties of wide binary stars, the probability that the Sun has a stellar companion capable of inducing periodic mass extinctions on Earth is only 0.05 percent. In an analogy with Oort cloud dynamics, I suggest a mechanism that can substantially reduce the number of wide binaries with separations greater than 0.1 parsec.

Molecular-dynamics simulation of the static pair-pair correlation function for classical fluids.

We have used a molecular-dynamics simulation to calculate the first seven nonzero Legendre coefficients, ${\mathit{Q}}^{(\mathit{l})}$(r,r'), of the static pair-pair correlation function Q(r,r'). The interaction potential was taken to be Lennard-Jones. The simulations were done at two different values of density and temperature, one coinciding with that of liquid argon near its triple point and the other with liquid argon at 181.0 K. Q(r,r') can be expressed in terms of two, three-, and four-body distribution functions. We use the Kirkwood superposition approximation to estimate the three-body contribution to Q(r,r'). We argue that at low densities the three-body correlations are substantially more important than the four-body correlations. The three-body part of the l=4 and 6 coefficients emphasizes configurations composed of nearest-neighbor triplets with internal angles of approximately 90\ifmmode^\circ\else\textdegree\fi{} and 60\ifmmode^\circ\else\textdegree\fi{}, respectively. We find that the l=6 coefficient shows a dramatic increase in structure at elevated density. Furthermore, this coefficient exhibits nearly periodic oscillations in its off-diagonal structure. Directions for future work are given.

Modified Lanczos simulation of the localized superconductivity for a chain with interaction and disorder.

Using the modified Lanczos algorithm, we calculate numerically for a chain with ten sites and half-filled the local pair-pair correlation function of the Anderson-Hubbard model (with the interaction both repulsive and attractive). The calculation aims to describe the phase with local superconductivity.

The structure of the ground state and low excited states of quantum fluids

The structure of the ground state of a quantum fluid is described in terms of the pair correlation function and pair-pair correlation function, which are the response functions to first and second order scattering respectively. Results are presented for the pair-pair correlation function of liquid 4He obtained using two methods: a Monte Carlo simulation and a hypernetted chain approximation. These results are used to obtain the solution of the Euler-Lagrange equation for the optimum Jastrow function for the ground state of liquid 4He. The Monte Carlo calculation is in good agreement with the augmented HNC approximation. General properties of the pair correlation function are discussed in terms of its Fourier transform, the liquid structure function. A critical review is given of the present status of the Jastrow theory (and its generalizations) of the ground state of boson and fermion quantum fluids. The recent extension of the Jastrow theory to include three-body factors by Pandharipande is compared to the earlier theory of Campbell, along with a parallel discussion of the theories of the low excited states of the boson fluid by Feynman and Cohen and by Jackson and Feenberg. The importance of the three-body factors to the quantitative agreement between the theoretical and experimental phonon-roton spectrum of liquid 4He is discussed.