Equation of state and Raman frequency of diamond from quantum Monte Carlo simulations

Imaging of the electronic bonding of diamond at pressures up to 2 million atmospheres

Diamond shows unprecedented hardness. Because hardness is a measure of resistance of chemical bonds in a material to external indentation, the electronic bonding nature of diamond beyond several million atmospheres is key to understanding the origin of hardness. However, probing the electronic structures of diamond at such extreme pressure has not been experimentally possible. The measurements on the inelastic x-ray scattering spectra for diamond up to 2 million atmospheres provide data on the evolution of its electronic structures under compression. The mapping of the observed electronic density of states allows us to obtain a two-dimensional image of the bonding transitions of diamond undergoing deformation. The spectral change near edge onset is minor beyond a million atmospheres, while its electronic structure displays marked pressure-induced electron delocalization. Such electronic responses indicate that diamond's external rigidity is supported by its ability to reconcile internal stress, providing insights into the origins of hardness in materials.

Probing anharmonic phonons by quantum correlators: A path integral approach

We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with the force-force quantum correlators and, in the weak anharmonic regime, yields reliable zero-point motion frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement-displacement correlators and accurately probes the lowest-energy phonon excitations, regardless of the anharmonicity strength of the system. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I4₁/amd phase of atomic hydrogen. We find that in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen.

Quantum vortex melting and superconductor insulator transition in a 2D Josephson junction array in a perpendicular magnetic field via diffusion Monte Carlo

In this study, we simulated a quantum rotor model describing a Josephson junction array (JJA) in the phase representation at zero temperature in a perpendicular magnetic field [Formula: see text] (in units of [Formula: see text]) on a [Formula: see text] square lattice with spacing a for [Formula: see text]. The superconductor-insulator transition (SIT) is tuned by the ratio of charging energy to Josephson coupling, U/J. Abrupt drops in the magnetization values were observed in the bigger lattices at certain values of B and U/J caused by the formation of vortices. Increasing U/J at a fixed B field causes quantum vortex melting. The magnetization drops to zero around [Formula: see text] indicating SIT. For B  =  0.1 the SIT occurs without an intermediate vortex state and the magnetization scales as [Formula: see text], whereas for B  =  0.4 the scaling is [Formula: see text] during the vortex melting. For B between 0.1 and 0.4 the scaling is not clear. We used the diffusion Monte Carlo (DMC) method with a guiding wavefunction optimized using the variational Monte Carlo (VMC) method. The ground state energy is calculated easily in DMC and its error estimates were generally smaller than [Formula: see text], both with and without the guiding wavefunction. Quantities like magnetization and vorticity that do not commute with the Hamiltonian were calculated using an efficient forward walking algorithm. Their estimates are affected severely in absence of the guiding wavefunction. With the guiding wavefunction, errors for the magnetization were generally less than [Formula: see text] and going up to [Formula: see text] percent around the phase transition from the Meissner to the vortex state, and without the guiding wavefunction errors were generally higher than [Formula: see text] and going up to [Formula: see text] around the critical point.

Fundamental high-pressure calibration from all-electron quantum Monte Carlo calculations

We develop an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and use it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We compute the static contribution to the free energy with the QMC method and obtain the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We compute the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy.

Methods for calculating forces within quantum Monte Carlo simulations

Atomic force calculations within the variational and diffusion quantum Monte Carlo methods are described. The advantages of calculating diffusion quantum Monte Carlo forces with the 'pure' rather than the 'mixed' probability distribution are discussed. An accurate and practical method for calculating forces using the pure distribution is presented and tested for the SiH molecule. The statistics of force estimators are explored and violations of the central limit theorem are found in some cases.

Benchmark quantum Monte Carlo calculations of the ground-state kinetic, interaction and total energy of the three-dimensional electron gas

We report variational and diffusion quantum Monte Carlo ground-state energies of the three-dimensional electron gas using a model periodic Coulomb interaction and backflow corrections for N = 54, 102, 178, and 226 electrons. We remove finite-size effects by extrapolation and we find lower energies than previously reported. Using the Hellman-Feynman operator sampling method introduced in Gaudoin and Pitarke (2007 Phys. Rev. Lett. 99 126406), we compute accurately, within the fixed-node approximation, the separate kinetic and interaction contributions to the total ground-state energy. The difference between the interaction energies obtained from the original Slater-determinant nodes and the backflow-displaced nodes is found to be considerably larger than the difference between the corresponding kinetic energies.

Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wavefunctions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well suited to implementation on petascale computers, and the computational cost scales as a polynomial in the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimization of wavefunctions, performing calculations under periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.

Total-energy minimization of few-body electron systems in the real-space finite-difference scheme

A practical and high-accuracy computation method to search for ground states of few-electron systems is presented on the basis of the real-space finite-difference scheme. A linear combination of Slater determinants is employed as a many-electron wavefunction, and the total-energy functional is described in terms of overlap integrals of one-electron orbitals without the constraints of orthogonality and normalization. In order to execute a direct energy minimization process of the energy functional, the steepest-descent method is used. For accurate descriptions of integrals which include bare-Coulomb potentials of ions, the time-saving double-grid technique is introduced. As an example of the present method, calculations for the ground state of the hydrogen molecule are demonstrated. An adiabatic potential curve is illustrated, and the accessibility and accuracy of the present method are discussed.

Dissociation energy of the water dimer from quantum Monte Carlo calculations

We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo techniques. We have performed variational quantum Monte Carlo and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP type single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mhartree, yielding a DMC energy of -76.428 30(5) hartree, which is only 10 mhartree above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger, and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcalmol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) D and dimer dipole moments which range between 2.628(6) and 2.672(5) D.

Energies of the first row atoms from quantum Monte Carlo

All-electron variational and diffusion quantum Monte Carlo calculations of the ground state energies of the first row atoms (from Li to Ne) are reported. The authors use trial wave functions of four types: single-determinant Slater-Jastrow wave functions, multideterminant Slater-Jastrow wave functions, single-determinant Slater-Jastrow wave functions with backflow transformations, and multideterminant Slater-Jastrow wave functions with backflow transformations. At the diffusion quantum Monte Carlo level and using their multideterminant Slater-Jastrow wave functions with backflow transformations, they recover 99% or more of the correlation energies for Li, Be, B, C, N, and Ne, 97% for O, and 98% for F.