Diffusion Monte Carlo Method Research Articles

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles.

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion MonteCarlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Diffusion Monte Carlo investigation of electronic structure properties for 13-atom alkali metal clusters

Electronic structure properties of 13-atom icosahedral alkali metal clusters (X13, X = Li, Na, K, Rb, and Cs) were investigated with the Diffusion Monte Carlo (DMC) and Density Functional Theory (DFT) methods. The overall results of vertical ionization energies, vertical electron affinities and dissociation energies are in good agreement with theoretical/experimental values found in the literature for these clusters. However, the DFT approach investigated, B3LYP, provides larger discrepancies than DMC for dissociation energies. In this case, empirical dispersion corrections seem important to improve the binding energy data from DFT. We also considered heteronuclear alkali metal clusters such as YX12, where the Y atom was placed at the center and also at the face of the initial icosahedral structure of X13. To our knowledge, the results for such heteronuclear clusters are being reported for the first time, providing an important initial step for understanding these systems. This work demonstrates that face-type YX12 clusters are usually more strongly bonded than the respective center-type structures, except for LiNa12, CsRb12, and KCs12 (according to DMC results). In addition, the trends evidenced in binding energies are analysed in details.

X(3872) ’s excitation and its connection with production at hadron colliders

The LHCb collaboration has found that the production rate of $X(3872)$ in proton-proton collisions decreases as final state particle multiplicity increases. Moreover, the ALICE experiment at CERN has observed that the number of deuterons produced increases with multiplicity, a behavior that is qualitatively different from that of the $X(3872)$. These experimental findings may point to a compact structure for the $X(3872)$ or, at least, that its hadronization could proceed through a charm-anticharm core. We have recently used a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation that describes the $X(3872)$ as a $c \bar c q \bar q$ tetraquark system with quantum numbers $I^G(J^{PC})=0^+(1^{++})$ and $1^-(1^{++})$. According to our structural analysis, the quark--(anti-)quark correlations resemble light-meson--heavy-meson molecules of type $\omega J/\psi$ and $\rho J/\psi$, rather than the most extended $D\bar D^{\ast}$ interpretation. It was argued that this fact may be the key to make compatible the molecular features of the $X(3872)$ with its production observables. The same formalism allows us to compute the first color excited $c \bar c q \bar q$ tetraquark state with either $I^G(J^{PC})=0^+(1^{++})$ or $1^-(1^{++})$. A bound-state is found in each channel, their masses are around 4.0 GeV which is an energy region where many new exotic candidates have been collected by the Particle Data Group. Concerning their structural properties, these states cluster in a compact diquark-antidiquark arrangement which matches perfectly with a so-called Born-Oppenheimer tetraquark configuration. The promptly production rates of these states in proton-proton, proton-nucleus and nucleus-nucleus collisions should fall off equal to or even faster than those of the $X(3872)$.

Van der Waals five-body size-energy universality

A universal relationship between scaled size and scaled energy is explored in five-body self-bound quantum systems. The ground-state binding energy and structure properties are obtained by means of the diffusion Monte Carlo method. We use pure estimators to eliminate any residual bias in the estimation of the cluster size. Strengthening the inter-particle interaction, we extend the exploration from the halo region to classical systems. Universal scaled size-scaled energy line, which does not depend on the short-range potential details and binding strength, is found for homogeneous pentamers with interaction potentials decaying at long range predominantly as r^{-6}. For mixed pentamers, we discuss under which conditions the universal line can approximately describe the size-energy ratio. Our data is compatible with generalized Tjon lines, which assume a linear dependence between the binding energy of the pentamers and the one of tetramers, when both are divided by the trimer energies.

Ab initio diffusion quantum Monte Carlo study of the structural and electronic properties of small Lithium-Chloride LinCl (0,1+) (n = 1–7) clusters

Superalkali metal clusters as the potential building blocks of nanostructured materials have excellent nonlinear optical properties. In the present study, the structural and electronic properties of small LinCl (0,1+) (n = 1–7) clusters are investigated by the diffusion Monte Carlo method for the first time. We calculate the total ground state energy, ionization potential, binding energy, dissociation energy, and second difference in energy. We also analyze the contribution of electron correlation effects to the electron properties of the clusters. The DMC results of ionization potentials are more consistent with the experimental values. In addition, there is an odd–even alternation phenomenon that Li3Cl, Li5Cl, and Li7Cl are more stable, while Li2Cl+, Li4Cl+, and Li6Cl+ are more stable. The successful application of the quantum Monte Carlo (QMC) method on the small LinCl (0,1+) (n = 1–7) clusters implies that QMC may serve as a feasible tool to investigate the electronic properties of other superalkli metal clusters.

The binding of atomic hydrogen on graphene from density functional theory and diffusion Monte Carlo calculations.

In this work, density functional theory (DFT) and diffusion Monte Carlo (DMC) methods are used to calculate the binding energy of a H atom chemisorbed on the graphene surface. The DMC value of the binding energy is about 16% smaller in magnitude than the Perdew-Burke-Ernzerhof (PBE) result. The inclusion of exact exchange through the use of the Heyd-Scuseria-Ernzerhof functional brings the DFT value of the binding energy closer in line with the DMC result. It is also found that there are significant differences in the charge distributions determined using PBE and DMC approaches.

Mixtures of Dipolar Gases in Two Dimensions: A Quantum Monte Carlo Study

We studied the miscibility of two dipolar quantum gases in the limit of zero temperature. The system under study is composed of a mixture of two Bose gases with dominant dipolar interaction in a two-dimensional harmonic confinement. The dipolar moments are all considered to be perpendicular to the plane, turning the dipolar potential in a purely repulsive and isotropic model. Our analysis is carried out by using the diffusion Monte Carlo method, which allows for an exact solution to the many-body problem within some statistical noise. Our results show that the miscibility between the two species is rather constrained as a function of the relative dipolar moments and masses of the two components. A narrow regime is predicted where both species mix and we introduce an adimensional parameter whose value quite accurately predicts the miscibility of the two dipolar gases.

A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

We study beryllium dihydride (BeH$_2$) and acetylene (C$_2$H$_2$) molecules using real-space diffusion Monte Carlo (DMC) method. The molecules serve as perhaps the simplest prototypes that illustrate the difficulties with biases in the fixed-node DMC calculations that might appear with the use of effective core potentials (ECPs) or other nonlocal operators. This is especially relevant for the recently introduced correlation consistent ECPs (ccECPs) for $2s2p$ elements. Corresponding ccECPs exhibit deeper potential functions due to higher fidelity to all-electron counterparts, which could lead to larger local energy fluctuations. We point out that the difficulties stem from issues that are straightforward to address by upgrades of basis sets, use of T-moves for nonlocal terms, inclusion of a few configurations into the trial function and similar. The resulting accuracy corresponds to the ccECP target (chemical accuracy) and it is in consistent agreement with independent correlated calculations. Further possibilities for upgrading the reliability of the DMC algorithm and considerations for better adapted and more robust Jastrow factors are discussed as well.

High Accuracy Transition Metal Effective Cores for the Many-Body Diffusion Monte Carlo Method.

Practical applications of the real-space diffusion Monte Carlo (DMC) method require the removal of core electrons, where currently localization approximations of semilocal potentials are generally used in the projector. Accurate calculations of complex solids and large molecules demand minimizing the impact of approximated atomic cores. Prior works have shown that the errors from such approximations can be sizable in both finite and periodic systems. In this work, we show that a class of differential pseudopotentials, known as pseudo-Hamiltonians, can be constructed for the 3d transition metal atoms, entirely removing the need for any localization scheme in the DMC projector. As a proof of principle, we demonstrate the approach for the case of Co. In order to minimize errors in the pseudo-Hamiltonian at the many-body level, we generalize the recently proposed correlation-consistent pseudopotential generation scheme to successively close semilocal representations of the differential potentials. Our generation scheme successfully produces potentials tailored specifically for real space projector quantum Monte Carlo methods with low error at the many-body level, i.e., with many-body scattering properties very close to relativistic all-electron results. In particular, we show that the agreement with respect to atomic and molecular quantities reach chemical accuracy in many cases─on par with the most accurate semilocal pseudopotentials available. Further, our pseudo-Hamiltonian generation scheme utilizes standard quantum chemistry codes designed only to work with semilocal pseudopotentials, enabling straightforward generation of pseudo-Hamiltonians for additional elements in future works.

Quantum-inspired diffusion Monte Carlo optimization algorithm applied to space trajectories and attitude maneuvers

In this work, an algorithm for solving optimization problems is proposed, inspired by a computational method employed in Quantum Mechanics: the Diffusion Monte Carlo method, commonly used for the computation of ground states of many-particle systems. The optimization problem is re-formulated as the problem of sampling the ground state wave function of a particle subject to a potential based on the function to be minimized. The algorithm is applied to problems in space trajectory and spacecraft attitude maneuvers optimization, the first application is to the problem of transfer between circular orbits, the results obtained are compared to the results from the literature, then it is applied to the problem of rendezvous with the asteroid Pallas, and finally to the optimization of an attitude maneuver in the presence of several constraints, and the obtained results are compared to two widely used methods: Particle Swarm Optimization and Differential Evolution algorithms. The algorithm is of simple implementation, and the numerical results show better performance than the comparison methods in the considered problems.

Diffusion Monte Carlo evaluation of disiloxane linearisation barrier.

The disiloxane molecule is a prime example of silicate compounds containing the Si-O-Si bridge. The molecule is of significant interest within the field of quantum chemistry, owing to the difficulty in theoretically predicting its properties. Herein, the linearisation barrier of disiloxane is investigated using a fixed-node diffusion Monte Carlo (FNDMC) approach, which is one of the most reliable ab initio methods in accounting for the electronic correlation. Calculations utilizing the density functional theory (DFT) and the coupled cluster method with single and double substitutions, including noniterative triples (CCSD(T)) are carried out alongside FNDMC for comparison. It is concluded that FNDMC successfully predicts the disiloxane linearisation barrier and does not depend on the completeness of the basis-set as much as DFT or CCSD(T), thus establishing its suitability.

A pathway toward high-throughput quantum Monte Carlo simulations for alloys: A case study of two-dimensional (2D) GaSxSe1-x.

The study of alloys using computational methods has been a difficult task due to the usually unknown stoichiometry and local atomic ordering of the different structures experimentally. In order to combat this, first-principles methods have been coupled with statistical methods such as the cluster expansion formalism in order to construct the energy hull diagram, which helps to determine if an alloyed structure can exist in nature. Traditionally, density functional theory (DFT) has been used in such workflows. In this paper, we propose to use chemically accurate many-body variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods to construct the energy hull diagram of an alloy system due to the fact that such methods have a weakerdependence on the starting wavefunction and density functional, scale similarly to DFT with the number of electrons, and have had demonstrated success for a variety of materials. To carry out these simulations in a high-throughput manner, we propose a method called Jastrow sharing, which involves recycling the optimized Jastrow parameters between alloys with different stoichiometries. We show that this eliminates the need for extra VMC Jastrow optimization calculations and results in significant computational cost savings (on average 1/4 savings of total computational time). Since it is a novel post-transition metal chalcogenide alloy series that has been synthesized in its few-layer form, we used monolayer GaSxSe1-x as a case study for our workflow. By extensively testing our Jastrow sharing procedure for monolayer GaSxSe1-x and quantifying the cost savings, we demonstrate how a pathway toward chemically accurate high-throughput simulations of alloys can be achieved using many-body VMC and DMC methods.

A diffusion Monte Carlo method for charge density on a conducting surface at non-constant potentials

Abstract We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.

Structure of the X(3872) as explained by a diffusion Monte Carlo calculation

Two decades after its unexpected discovery, the properties of the $X(3872)$ exotic resonance are still under intense scrutiny. In particular, there are doubts about its nature as an ensemble of mesons or having any other internal structure. We use a Diffusion Monte Carlo method to solve the many-body Schr\"odinger equation that describes this state as a $c \bar c n \bar n$ ($n=u$ or $d$ quark) system. This approach accounts for multi-particle correlations in physical observables avoiding the usual quark-clustering assumed in other theoretical techniques. The most general and accepted pairwise Coulomb$\,+\,$linear-confining$\,+\,$hyperfine spin-spin interaction, with parameters obtained by a simultaneous fit of around 100 masses of mesons and baryons, is used. The $X(3872)$ contains light quarks whose masses are given by the mechanism responsible of the dynamical breaking of chiral symmetry. The same mechanisms gives rise to Goldstone-boson exchange interactions between quarks that have been fixed in the last 10-20 years reproducing hadron, hadron-hadron and multiquark phenomenology. It appears that a meson-meson molecular configuration is preferred but, contrary to the usual assumption of $D^0\bar{D}^{\ast0}$ molecule for the $X(3872)$, our formalism produces $\omega J/\psi$ and $\rho J/\psi$ clusters as the most stable ones, which could explain in a natural way all the observed features of the $X(3872)$.

Dilute quantum liquid in a K-Rb Bose mixture

A quantum liquid in a heterogeneous mixture of $^{41}$K and $^{87}$Rb atoms is studied using the diffusion Monte Carlo method and Density Functional Theory. The perturbative Lee-Huang-Yang term for a heterogeneous mixture is verified and it is proved to be valid only near the gas-liquid transition. Based on the equations of state of the bulk mixture, calculated with diffusion Monte Carlo, extensions to Lee-Huang-Yang corrected mean-field energy functionals (MF+LHY) are presented. Using Density Functional Theory, a systematic comparison between different functionals is performed, focusing on the critical atom number, surface tension, surface width, Tolman length, and compressibility. These results are given as a function of the inter-species interaction strength, within the stability domain of the liquid mixture.

Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum MonteCarlo.

According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion MonteCarlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.

Nuclear energy density functionals grounded in ab initio calculations

We discuss the construction of a nuclear Energy Density Functional (EDF) from ab initio calculations, and we advocate the need of a methodical approach that is free from ad hoc assumptions. The equations of state (EoS) of symmetric nuclear and pure neutron matter are computed using the chiral NNLO$_{\rm sat}$ and the phenomenological AV4$^\prime$+UIX$_{c}$ Hamiltonians as inputs in the Self-consistent Green's Function (SCGF) and Auxiliary Field Diffusion Monte Carlo (AFDMC) methods, respectively. We propose a convenient parametrization of the EoS as a function of the Fermi momentum and fit it on the SCGF and AFDMC calculations. We apply the ab initio-based EDF to carry out an analysis of the binding energies and charge radii of different nuclei in the local density approximation. The NNLO$_{\rm sat}$-based EDF produces encouraging results, whereas the AV4$^\prime$+UIX$_{c}$-based one is farther from experiment. Possible explanations of these different behaviors are suggested, and the importance of gradient and spin-orbit terms is analyzed. Our work paves the way for a practical and systematic way to merge ab initio nuclear theory and DFT, while at the same time it sheds light on some of the critical aspects of this procedure.

Multiscale quantum harmonic oscillator optimization algorithm with multiple quantum perturbations for numerical optimization

Multi-scale quantum harmonic oscillator algorithm (MQHOA) is a recent proposed intelligent algorithm, in which the optimization process can be regarded as the multi-scale quantum annealing process with respect to the constraint of the harmonic oscillator potential well. It has been proved effective and efficient to deal with unimodal and multimodal numerical optimization problems. However, it takes a long time for the particles system to reach the ground-state equilibrium at each annealing scale. Motivated by this situation, a diffusion Monte Carlo method based dynamic sampling regulation strategy is proposed to enhances the sampling efficiency by dynamically adjusting the sampling frequency. Moreover, the particles with different kinetic energies are introduced into the optimization system as quantum perturbations, which reduces the probability of the algorithm falling into a local optimum by keeping the different searching scales simultaneously. The theoretical derivations of this method are presented. The effectiveness of the algorithm is studied by comparing it with previous versions of the MQHOA and several famous intelligent algorithms on uni- and multimodal benchmark functions. The experimental results illustrate that the proposed method has a comparable performance for numerical optimization problems.

Ab initio investigation on the low-lying states of LaX (X = Se, Sn, Sb)

Potential energy curves for the low-lying electronic states of the title molecules in their neutral and anionic forms have been calculated by means of the diffusion Monte Carlo method. The effect of different trial functionals has been investigated using single determinants constructed from density functional theory (DFT) orbitals with B3LYP, B3PW91, and M06-2X functions. Bond length, vibrational frequency, and electron affinity have also been numerically derived for the selected species and the ground state has been assigned. Spectroscopic parameters obtained are interpreted and compared to their isovalents, shedding some light on further investigations on the selected dimers.

CrI3 revisited with a many-body ab initio theoretical approach

${\mathrm{CrI}}_{3}$ has recently been shown to exhibit low-dimensional, long-range magnetic ordering from few layers to single layers of ${\mathrm{CrI}}_{3}$. The properties of ${\mathrm{CrI}}_{3}$ bulk and few-layered systems are uniquely defined by a combination of short-range intralayer and long-range interlayer interactions, including strong correlations, exchange, and spin-orbit coupling. Unfortunately, both the long-range van der Waals interactions, which are driven by dynamic, many-body electronic correlations, and the competing strong intralayer correlations, present a formidable challenge for the local or semilocal mean-field approximations employed in workhorse electronic structure approaches like density-functional theory. In this paper we employ a sophisticated many-body approach that can simultaneously describe long- and short-range correlations. We establish that the fixed-node diffusion Monte Carlo (FNDMC) method reproduces the experimental interlayer separation distance of bulk ${\mathrm{CrI}}_{3}$ for the high-temperature monoclinic phase with a reliable prediction of the interlayer binding energy. We subsequently employed the FNDMC results to benchmark the accuracy of several density-functional theory exchange-correlation approximations.