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We present a study of spin-unpolarized and spin-polarized two-dimensional uniform electron liquids using variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions. Ground-state VMC and DMC energies are obtained in the density range $1 \leq r_\text{s} \leq 40$. Single-particle and many-body finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of twist-averaged energies to the thermodynamic limit of infinite system size. System-size-dependent errors in Slater-Jastrow-backflow DMC energies caused by partially converged VMC energy minimization calculations are discussed. We find that, for $1 \leq r_\text{s} \leq 5$, optimizing the backflow function at each twist lowers the twist-averaged DMC energy at finite system size. However, nonsystematic system-size-dependent effects remain in the DMC energies, which can be partially removed by extrapolation from multiple finite system sizes to infinite system size. We attribute these nonsystematic effects to the close competition between fluid and defected crystal phases at different system sizes at low density. The DMC energies in the thermodynamic limit are used to parameterize a local spin density approximation correlation functional for inhomogeneous electron systems. Our zero-temperature phase diagram shows a single transition from a paramagnetic fluid to a hexagonal Wigner crystal at $r_\text{s}=35(1)$, with no region of stability for a ferromagnetic fluid.

We analyze the scattering of light from dipolar emitters whose disordered positions exhibit correlations induced by static, long-range dipole-dipole interactions. The quantum-mechanical position correlations are calculated for zero temperature bosonic atoms or molecules using variational and diffusion quantum Monte Carlo methods. For stationary atoms in dense ensembles in the limit of low light intensity, the simulations yield solutions for the optical responses to all orders of position correlation functions that involve electronic ground and excited states. We calculate how coherent and incoherent scattering, collective linewidths, line shifts, and eigenmodes, and disorder-induced excitation localization are influenced by the static interactions and the density. We find that dominantly repulsive static interactions in strongly confined oblate and prolate traps introduce short-range ordering among the dipoles which curtails large fluctuations in the light-mediated resonant dipole-dipole interactions. This typically results in an increase in coherent reflection and optical depth, accompanied by reduced incoherent scattering. The presence of static dipolar interactions permits the highly selective excitation of subradiant eigenmodes in dense clouds. This effect becomes even more pronounced in a prolate trap, where the resonances narrow below the natural linewidth. When the static dipolar interactions affect the optical transition frequencies, the ensemble exhibits inhomogeneous broadening due to the nonuniformly experienced static dipolar interactions that suppress cooperative effects, but we argue that, e.g., for Dy atoms such inhomogeneous broadening is negligible., Comment: Expanded experimental considerations, etc

Variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions are used to study the spin-polarized three-dimensional uniform electron fluid. We report ground state VMC and DMC energies in the density range $0.5 \leq r_\text{s} \leq 20$. Finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of the twist-averaged energy per particle calculated at three system sizes (N=113, 259, and 387) to the thermodynamic limit of infinite system size. The DMC energies in the thermodynamic limit are used to parameterize a local spin density approximation correlation function for inhomogeneous electron systems., Comment: arXiv admin note: substantial text overlap with arXiv:2209.10227

We use the variational quantum Monte Carlo (VMC) method to study the wire width ($b$) and electron density ($r_\text{s}$) dependences of the ground-state properties of quasi-one-dimensional paramagnetic electron fluids. The onset of a quasi-Wigner crystal phase is known to depend on electron density, and the crossover occurs in the low density regime. We study the effect of wire width on the crossover of the dominant peak in the static structure factor from $k=2k_\text{F}$ to $k=4k_\text{F}$. It is found that for a fixed electron density, in the charge structure factor the crossover from the dominant peak occurring at $2k_\text{F}$ to $4k_\text{F}$ occurs as the wire width decreases. Our study suggests that the crossover is due to interplay of both $r_\text{s}$ and $b

The variational and diffusion quantum Monte Carlo methods are used to calculate the correlation energy of the paramagnetic three-dimensional homogeneous electron gas at intermediate to high density. Ground state energies in finite cells are determined using Slater-Jastrow-backflow trial wave functions, and finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Our correlation energies in the thermodynamic limit are lower (i.e., more negative, and therefore more accurate according to the variational principle) than previous results, and can be used for the parameterization of density functionals to be applied to high-density systems.

Three-dimensional (3D) excitonic complexes influence the optoelectronic properties of bulk semiconductors. More generally, correlated few-particle molecules and ions, held together by pairwise Coulomb potentials, play a fundamental role in a variety of fields in physics and chemistry. Based on statistically exact diffusion quantum Monte Carlo calculations, we have studied excitonic three- and four-body complexes (trions and biexcitons) in bulk 3D semiconductors as well as a range of small molecules and ions in which the nuclei are treated as quantum particles on an equal footing with the electrons. We present interpolation formulas that predict the binding energies of these complexes either in bulk semiconductors or in free space. By evaluating pair distribution functions within quantum Monte Carlo simulations, we examine the importance of harmonic and anharmonic vibrational effects in small molecules.

The photoluminescence (PL) spectra of monolayer (1L) semiconductors feature peaks ascribed to different charge-carrier complexes. We perform diffusion quantum Monte Carlo simulations of the binding energies of these complexes and examine their response to electric and magnetic fields. We focus on quintons (charged biexcitons), since they are the largest free charge-carrier complexes in transition-metal dichalcogenides (TMDs). We examine the accuracy of the Rytova-Keldysh interaction potential between charges by comparing the binding energies of charge-carrier complexes in 1L-TMDs with results obtained using $\textit{ab initio}$ interaction potentials. Magnetic fields$<8$T change the binding energies (BEs) by$\sim0.2$ meV,T$^{-1}$, in agreement with experiments, with the BE variations of different complexes being very similar. Our results will help identify charge complexes in the PL spectra of 1L-semiconductors

We present an analysis of positron lifetimes in solids with unprecedented depth. Instead of modeling correlation effects with density functionals, we study positron-electron wave functions with long-range correlations included. This gives new insight in understanding positron annihilation in metals, insulators and semiconductors. By using a new quantum Monte Carlo approach for computation of positron lifetimes, an improved accuracy compared to previous computations is obtained for a representative set of materials when compared with experiment. Thus we present a method without free parameters as a useful alternative to the already existing methods for modeling positrons in solids.

Deep neural networks have been extremely successful as highly accurate wave function ans\"atze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network is given no \emph{a priori} knowledge that a phase transition exists, but converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density., Comment: 12 pages, 3 figures

Variational and diffusion quantum Monte Carlo methods are employed to investigate the zero-temperature phase diagram of the three-dimensional homogeneous electron gas at very low density. Fermi fluid and body-centered cubic Wigner crystal ground state energies are determined using Slater-Jastrow-backflow and Slater-Jastrow many-body wave functions at different densities and spin polarizations in finite simulation cells. Finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Unlike previous studies, our results show that the electron gas undergoes a first-order quantum phase transition directly from a paramagnetic fluid to a body-centered cubic crystal at density parameter $r_\text{s} = 86.6(7)$, with no region of stability for an itinerant ferromagnetic fluid. However there is a possible magnetic phase transition from an antiferromagnetic crystal to a ferromagnetic crystal at $r_\text{s}=93(3)$., Comment: accepted for publication

Density functional theory (DFT) is widely used to study defects in monolayer graphene with a view to applications ranging from water filtration to electronics to investigation of radiation damage in graphite moderators. To assess the accuracy of DFT in such applications, we report diffusion quantum Monte Carlo (DMC) calculations of the formation energies of some common and important point defects in monolayer graphene: monovacancies, Stone-Wales defects, and silicon substitutions. We find that standard DFT methods underestimate monovacancy formation energies by around 1 eV. The disagreement between DFT and DMC is somewhat smaller for Stone-Wales defects and silicon substitutions. We examine vibrational contributions to the free energies of formation for these defects, finding that vibrational effects are non-negligible. Finally, we compare the DMC atomization energies of monolayer graphene, monolayer silicene, and bulk silicon, finding that bulk silicon is significantly more stable than monolayer silicene by 0.7522(5) eV per atom.

We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths $b$ and density parameters $r_\text{s}$. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density, $r_\text{s}=0.5$. It is observed that the peak in the static structure factor at $k=2k_\text{F}$ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter $K_\rho$ from the momentum density. It is found that $K_\rho$ increases by about $10$\% between wire widths $b=0.01$ and $b=0.5$. We also obtain ground-state properties of finite thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b \ll r_\text{s}<1$. It is found that the correlation energy varies as $b^2$ for $b \ll r_\text{s}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of $b$ and $r_\text{s} \leq 1$. These are compared with the QMC results in the range of applicability of the theory.

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 work, we deploy diffusion Monte Carlo (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., Comment: Accepted for the publication

The correlation between electrons in different quantum wires is expected to affect the electronic properties of quantum electron-electron biwire systems. Here, we use the variational Monte Carlo method to study the ground-state properties of parallel, infinitely thin electron-electron biwires for several electron densities ($r_\text{s}$) and interwire separations ($d$). Specifically, the ground-state energy, the correlation energy, the interaction energy, the pair-correlation function (PCF), the static structure factor (SSF), and the momentum distribution (MD) function are calculated. We find that the interaction energy increases as $\ln(d)$ for $d\to 0$ and it decreases as $d^{-2}$ when $d\to \infty$. The PCF shows oscillatory behavior at all densities considered here. As two parallel wires approach each other, interwire correlations increase while intrawire correlations decrease as evidenced by the behavior of the PCF, SSF, and MD. The system evolves from two monowires of density parameter $r_\text{s}$ to a single monowire of density parameter $r_\text{s}/2$ as $d$ is reduced from infinity to zero. The MD reveals Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near $k_\text{F}$ even in the presence of an extra interwire interaction between the electrons in biwire systems. It is observed that when $d$ is reduced the MD decreases for $kk_\text{F}$, similar to its behavior with increasing $r_\text{s}$. The TL liquid exponent is extracted by fitting the MD data near $k_\text{F}$, from which the TL liquid interaction parameter $K_{\rho}$ is calculated. The value of the TL parameter is found to be in agreement with that of a single wire for large separation between the two wires.

We use dispersion-corrected density-functional theory to determine the relative energies of competing polytypes of bulk layered hexagonal post-transition-metal chalcogenides, to search for the most stable structures of these potentially technologically important semiconductors. We show that there is some degree of consensus among dispersion-corrected exchange-correlation functionals regarding the energetic orderings of polytypes, but we find that for each material there are multiple stacking orders with relative energies of less than 1 meV per monolayer unit cell, implying that stacking faults are expected to be abundant in all post-transition-metal chalcogenides. By fitting a simple model to all our energy data, we predict that the most stable hexagonal structure has P$6_3$/mmc space group in each case, but that the stacking order differs between GaS, GaSe, GaTe, and InS on the one hand and InSe and InTe on the other. At zero pressure, the relative energies obtained with different functionals disagree by around 1-5 meV per monolayer unit cell, which is not sufficient to identify the most stable structure unambiguously; however, multi-GPa pressures reduce the number of competing phases significantly. At higher pressures, an AB$'$-stacked structure of the most stable monolayer polytype is found to be the most stable bulk structure; this structure has not been reported in experiments thus far.

We report diffusion quantum Monte Carlo (DMC) and many-body $GW$ calculations of the electronic band gaps of monolayer and bulk hexagonal boron nitride (hBN). We find the monolayer band gap to be indirect. $GW$ predicts much smaller quasiparticle gaps at both the single-shot $G_0W_0$ and the partially self-consistent $GW_0$ levels. In contrast, solving the Bethe-Salpeter equation on top of the $GW_0$ calculation yields an exciton binding energy for the direct exciton at the $K$ point in close agreement with the DMC value. Vibrational renormalization of the electronic band gap is found to be significant in both the monolayer and the bulk. Taking vibrational effects into account, DMC overestimates the band gap of bulk hBN, while $GW$ theory underestimates it.

We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and their weaknesses. We review a range of recent applications of CASINO.

We calculate the ground-state energy, pair correlation function, static structure factor, and momentum density of the one-dimensional electron fluid at high density using variational quantum Monte Carlo simulation. For an infinitely thin cylindrical wire the predicted correlation energy is found to fit nicely with a quadratic function of coupling parameter $r_s$. The extracted exponent $\alpha$ of the momentum density for $k\sim k_F$ is used to determine the Tomonaga-Luttinger parameter $K_\rho$ as a function of $r_s$ in the high-density regime for the first time. We find that the simulated static structure factor and pair correlation function for infinitely thin wires agree with our recent high-density theory [K. Morawetz et al., Phys. Rev. B 97, 155147 (2018)].

Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schr\"odinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods., Comment: 23 pages, 9 figures, 11 tables

We present density functional theory calculations of the binding energies of one, two and three fluorine adatoms on the same side of monolayer graphene. We show that fluorine dimers on graphene in a spin-singlet state are stable against dissociation into isolated fluorine adatoms, suggesting that there is a tendency for fluorine adatoms on a single side of graphene to cluster. Our results suggest that fluorination develops by successive bonding of fluorine atoms to neighbouring carbon atoms on different sublattices, while the spins are arranged to reduce the total magnetisation of the ground state. We find that the finite-size error in the binding energy of a single fluorine atom or dimer on a periodic supercell of graphene scales inversely with the cube of the linear size of the simulation supercell. By using $\pi$-orbital axis analysis, the rehybridisation of the three $\sigma$-orbitals pointing directly along the bonds to the central fluorinated carbon is found to be sp\textsuperscript{2.33}. The rehybridisation of the carbon orbital in the C--F bond is found to be sp\textsuperscript{4.66}., Comment: 14 pages, 3 figuers

We report variational and diffusion quantum Monte Carlo calculations of the binding energies of indirect trions and biexcitons in ideal two-dimensional bilayer systems within the effective-mass approximation, and with a Coulomb $1/r$ interaction between charge carriers. The critical layer separation at which trions become unbound has been studied for various electron-hole mass ratios, and found to be over an order of magnitude larger than the critical layer separation for biexcitons.

Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide (i) statistically exact diffusion quantum Monte Carlo binding-energy data for a Mott-Wannier model of (donor/acceptor-bound) excitons, trions, and biexcitons in two-dimensional semiconductors in which charges interact via the Keldysh potential, (ii) contact pair-distribution functions to allow a perturbative description of contact interactions between charge carriers, and (iii) an analysis and classification of the different types of bright trion and biexciton that can be seen in single-layer molybdenum and tungsten dichalcogenides. We investigate the stability of biexcitons in which two charge carriers are indistinguishable, finding that they are only bound when the indistinguishable particles are several times heavier than the distinguishable ones. Donor/acceptor-bound biexcitons have similar binding energies to the experimentally measured biexciton binding energies. We predict the relative positions of all stable free and bound excitonic complexes of distinguishable charge carriers in the photoluminescence spectra of WSe$_2$ and MoSe$_2$.

Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional (2D) semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide statistically exact diffusion quantum Monte Carlo binding-energy data for Mott-Wannier models of excitons, trions, and biexcitons in 2D semiconductors. We also provide contact pair densities to allow a description of contact (exchange) interactions between charge carriers using first-order perturbation theory. Our data indicate that the binding energy of a trion is generally larger than that of a biexciton in 2D semiconductors. We provide interpolation formulas giving the binding energy and contact density of 2D semiconductors as functions of the electron and hole effective masses and the in-plane polarizability., Comment: 5 pages

We present an accurate study of the static-nucleus electronic energy band gap of solid molecular hydrogen at high pressure. The excitonic and quasiparticle gaps of the $C2/c$, $Pc$, $Pbcn$, and $P6_3/m$ structures at pressures of 250, 300, and 350~GPa are calculated using the fixed-node diffusion quantum Monte Carlo (DMC) method. The difference between the mean-field and many-body band gaps at the same density is found to be almost independent of system size and can therefore be applied as a scissor correction to the mean-field gap of an infinite system to obtain an estimate of the many-body gap in the thermodynamic limit. By comparing our static-nucleus DMC energy gaps with available experimental results, we demonstrate the important role played by nuclear quantum effects in the electronic structure of solid hydrogen. Our DMC results suggest that the metallization of high-pressure solid hydrogen occurs via a structural phase transition rather than band gap closure.

We report a systematic analysis of the performance of a widely used set of Dirac-Fock pseudopotentials for quantum Monte Carlo (QMC) calculations. We study each atom in the periodic table from hydrogen (Z=1) to mercury (Z=80), with the exception of the 4f elements (57 <= Z <= 70). We demonstrate that ghost states are a potentially serious problem when plane-wave basis sets are used in density functional theory (DFT) orbital-generation calculations, but that this problem can be almost entirely eliminated by choosing the s channel to be local in the DFT calculation; the d channel can then be chosen to be local in subsequent QMC calculations, which generally leads to more accurate results. We investigate the achievable energy variance per electron with different levels of trial wave function and we determine appropriate plane-wave cutoff energies for DFT calculations for each pseudopotential. We demonstrate that the so-called "T-move" scheme in diffusion Monte Carlo is essential for many elements. We investigate the optimal choice of spherical integration rule for pseudopotential projectors in QMC calculations. The information reported here will prove crucial in the planning and execution of QMC projects involving beyond-first-row elements.

We report diffusion quantum Monte Carlo (DMC) calculations of the quasiparticle and excitonic gaps of hydrogen-terminated oligoynes and polyyne. The electronic gaps are found to be very sensitive to the atomic structure in these systems. We have therefore optimised the geometry of polyyne by directly minimising the DMC energy with respect to the lattice constant and the Peierls-induced carbon-carbon bond-length alternation. We find the bond-length alternation of polyyne to be 0.136(2) {\AA} and the excitonic and quasiparticle gaps to be 3.30(7) and 3.4(1) eV, respectively. The DMC zone-centre longitudinal optical phonon frequency of polyyne is 2084(5) cm$^{-1}$, which is consistent with Raman spectroscopic measurements for large oligoynes., Comment: 13 pages and 14 figures

Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is nonmetallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.

We report diffusion quantum Monte Carlo calculations of the interlayer binding energy of bilayer graphene. We find the binding energies of the AA- and AB-stacked structures at the equilibrium separation to be 11.5(9) and 17.7(9) meV/atom, respectively. The out-of-plane zone-center optical phonon frequency predicted by our binding-energy curve is consistent with available experimental results. As well as assisting the modeling of interactions between graphene layers, our results will facilitate the development of van der Waals exchange-correlation functionals for density functional theory calculations., Comment: 5 pages and 3 figures, submitted to Phys. Rev. Lett.; supplemental material is available on arXiv via the ancillary files attached to this submission

The interaction between a single hole and a two-dimensional, paramagnetic, homogeneous electron gas is studied using diffusion quantum Monte Carlo simulations. Calculations of the electron-hole correlation energy, pair-correlation function, and the electron-hole center-of-mass momentum density are reported for a range of electron--hole mass ratios and electron densities. We find numerical evidence of a crossover from a collective Mahan exciton to a trion-dominated state in a density range in agreement with that found in recent experiments on quantum well heterostructures., Comment: Final author version. 6 figures. Minor changes in this version include slightly expanded discussion of the peak in the momentum density in the supplemental material. Supplemental material is available on arXiv via the ancillary files attached to this submission

We use density functional theory to calculate the electronic band structures, cohesive energies, phonon dispersions, and optical absorption spectra of two-dimensional In$_2$X$_2$ crystals, where X is S, Se, or Te. We identify two crystalline phases (alpha and beta) of monolayers of hexagonal In$_2$X$_2$, and show that they are characterized by different sets of Raman-active phonon modes. We find that these materials are indirect-band-gap semiconductors with a sombrero-shaped dispersion of holes near the valence-band edge. The latter feature results in a Lifshitz transition (a change in the Fermi-surface topology of hole-doped In$_2$X$_2$) at hole concentrations $n_{\rm S}=6.86\times 10^{13}$ cm$^{-2}$, $n_{\rm Se}=6.20\times 10^{13}$ cm$^{-2}$, and $n_{\rm Te}=2.86\times 10^{13}$ cm$^{-2}$ for X=S, Se, and Te, respectively, for alpha-In$_2$X$_2$ and $n_{\rm S}=8.32\times 10^{13}$ cm$^{-2}$, $n_{\rm Se}=6.00\times 10^{13}$ cm$^{-2}$, and $n_{\rm Te}=8.14\times 10^{13}$ cm$^{-2}$ for beta-In$_2$X$_2$., Comment: 9 pages. arXiv admin note: text overlap with arXiv:1302.6067

Solid He is studied in the pressure and temperature ranges 1-40 TPa and 0-10,000 K using first-principles methods. Anharmonic vibrational properties are calculated within a self-consistent field framework, including the internal and free energies, density-pressure relation, stress tensor, thermal expansion, and the electron-phonon coupling renormalization of the electronic band gap. We find that an accurate description of electron-phonon coupling requires us to use a non-perturbative approach. The metalization pressure of 32.9 TPa at 0 K is larger than found previously. The vibrational effects are large; for example at P=30 TPa the band gap is increased by 2.8 eV by electron-phonon coupling and a further 0.1 eV by thermal expansion compared to the static value. The implications of the calculated metalization pressure for the cooling of white dwarfs are discussed., Comment: 5 pages, 6 figures

We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used twist averaging to reduce finite-size effects. Calculations of the pair correlation function, including the on-top pair density, as well as the structure factor and the total energy, are reported for systems of 118 electrons in the density range $r_\text{s}=0.5$--20 a.u., and for spin polarizations of 0, 0.34, 0.66, and 1. We consider the spin resolution of the pair correlation function and structure factor, and the energy of spin polarization. We show that a control variate method can reduce the variance when twist-averaging, and we have achieved higher accuracy and lower noise than earlier quantum Monte Carlo studies., Comment: 10 pages; 12 figures in color. Submitted to Phys. Rev. B

Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of "best available" values for the Fermi liquid parameters., Comment: 11 pages

A unified approach is used to study vibrational properties of periodic systems with first-principles methods and including anharmonic effects. Our approach provides a theoretical basis for the determination of phonon-dependent quantities at finite temperatures. The low-energy portion of the Born-Oppenheimer energy surface is mapped and used to calculate the total vibrational energy including anharmonic effects, electron-phonon coupling, and the vibrational contribution to the stress tensor. We report results for the temperature dependence of the electronic band gap and the linear coefficient of thermal expansion of diamond, lithium hydride, and lithium deuteride., Comment: 11 pages, 7 figures

We report density-functional-theory calculations of the electronic band structures and optical absorption spectra of two-dimensional crystals of Ga$_2$X$_2$ (X=S, Se, and Te). Our calculations show that all three two-dimensional materials are dynamically stable indirect-band-gap semiconductors with a Mexican-hat dispersion of holes near the top of the valence band. We predict the existence of Lifshitz transitions---changes in the Fermi-surface topology of hole-doped Ga$_2$X$_2$---at hole concentrations $n_{S}=7.96\times 10^{13}$ cm$^{-2}$, $n_{Se}=6.13\times 10^{13}$ cm$^{-2}$, and $n_{Te}=3.54\times 10^{13}$ cm$^{-2}$.

The quasiparticle effective mass is a key quantity in the physics of electron gases, describing the renormalization of the electron mass due to electron-electron interactions. Two-dimensional electron gases are of fundamental importance in semiconductor physics, and there have been numerous experimental and theoretical attempts to determine the quasiparticle effective mass in these systems. In this work we report quantum Monte Carlo results for the quasiparticle effective mass of a two-dimensional homogeneous electron gas. Our calculations differ from previous quantum Monte Carlo work in that much smaller statistical error bars have been achieved, allowing for an improved treatment of finite-size effects. In some cases we have also been able to use larger system sizes than previous calculations.

We report calculations of the electronic structure of silicene and the stability of its weakly buckled honeycomb lattice in an external electric field oriented perpendicular to the monolayer of Si atoms. We find that the electric field produces a tunable band gap in the Dirac-type electronic spectrum, the gap being suppressed by a factor of about eight by the high polarizability of the system. At low electric fields, the interplay between this tunable band gap, which is specific to electrons on a honeycomb lattice, and the Kane-Mele spin-orbit coupling induces a transition from a topological to a band insulator, whereas at much higher electric fields silicene becomes a semimetal.

We have computed the absorption and emission energies and hence Stokes shifts of small diamondoids as a function of size using different theoretical approaches, including density functional theory and quantum Monte Carlo (QMC) calculations. The absorption spectra of these molecules were also investigated by time-dependent density functional theory (TD-DFT) and compared with experiment. We have analyzed the structural distortion and formation of a self-trapped exciton in the excited state, and we have studied the effects of these on the Stokes shift as a function of size. Compared to recent experiments, QMC overestimates the excitation energies by about 0.8(1) eV on average. Benefiting from a cancellation of errors, the optical gaps obtained in DFT calculations with the B3LYP functional are in better agreement with experiment. It is also shown that TD-B3LYP calculations can reproduce most of the features found in the experimental spectra. According to our calculations, the structures of diamondoids in the excited state show a distortion which is hardly noticeable compared to that found for methane. As the number of diamond cages is increased, the distortion mechanism abruptly changes character. We have shown that the Stokes shift is size-dependent and decreases with the number of diamond cages. The rate of decrease in the Stokes shift is on average 0.1 eV per cage for small diamondoids., Comment: 29 pages,6 figures,3 tables

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects., Comment: 5 pages

We present calculations of the energy, pair correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer-multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around the Fermi wave vector, finding good agreement between the exponent of the ferromagnetic infinitely-thin wire and the ferromagnetic harmonic wire., Comment: 13 pages, 16 figures, 5 tables

Motivated by potential realizations in cold-atom or cold-molecule systems, we have performed quantum Monte Carlo simulations of two-component gases of fermions in two dimensions with hard-core interactions. We have determined the gross features of the zero-temperature phase diagram, by investigating the relative stabilities of paramagnetic and ferromagnetic fluids and crystals. We have also examined the effect of including a pairwise, long-range r^(-3) potential between the particles. Our most important conclusion is that there is no region of stability for a ferromagnetic fluid phase, even if the long-range interaction is present. We also present results for the pair-correlation function, static structure factor, and momentum density of two-dimensional hard-core fluids.

We have studied the diamond -> beta-tin phase transition in Si using diffusion quantum Monte Carlo (DMC) methods. Slater-Jastrow-backflow trial wave functions give lower DMC energies than Slater-Jastrow ones, and backflow slightly favors the beta-tin phase with respect to the diamond phase. We have investigated the changes in the equation of state that result from the use of different pseudopotentials, the inclusion of either zero-point motion or finite-temperature vibrations, and the application of corrections for finite-size effects. Our tests indicate that the choice of pseudopotential can significantly affect the equation of state. Using a Dirac-Fock pseudopotential leads to an overestimation of the transition pressure but an empirical pseudopotential designed for use in correlated calculations gives a transition pressure in quite good agreement with experiment., Comment: 2 figures

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03 %, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV per formula unit. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1 %., Comment: 16 pages, 4 figures

We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte Carlo method. Our finding that a relative time-step ratio of 1:4 is optimal in DMC is in agreement with the result of [J. Vrbik and S.M.Rothstein, Intern. J. Quantum Chem. 29, 461-468 (1986)]. Finally, we discuss the removal of serial correlation from data sets by reblocking, setting out criteria for the choice of block length and quantifying the effects of the uncertainty in the estimated correlation length., Comment: 12 pages, 5 figures

Calculations of the relaxation energy, contact pair-correlation function, and annihilating-pair momentum density for a single positron immersed in a homogeneous electron gas are presented. We achieve an accurate description of the electron-positron correlation effects by working in the reference frame in which the positron is stationary and using a mean-field approach based on single-component density functional theory. Our positron relaxation energies and annihilation rates are similar to those from the best existing many-body calculations. Our annihilating-pair momentum densities are significantly different from previous data, and include a "tail" beyond the Fermi edge.

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of 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 optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair correlation function, static structure factor, and momentum density of the ground state of the two-dimensional homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.

We have used quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter r_s=31(1) a.u. and a transition to a ferromagnetic crystal at r_s=38(5) a.u. The fully spin-polarized fluid is never stable. We searched for, but did not find, the ferromagnetic hybrid phase proposed by H. Falakshahi and X. Waintal [Phys. Rev. Lett. 94, 046801 (2005)].