Neil D. Drummond

The Baldereschi point of a crystal is a wavevector in the Brillouin zone (BZ) at which every smooth periodic function of wavevector lies close to its mean value. Although originally introduced in the context of one-electron methods, mean-value points are ideal for explicitly correlated many-electron methods such as quantum Monte Carlo simulations, which can only use a single Bloch wavevector in the BZ of a simulation supercell. We have therefore evaluated and tabulated the Baldereschi mean-value points of all fourteen three-dimensional Bravais lattices.

Using the Kohn-Sham (KS) inversion method of Hollins [], we invert densities from variational and diffusion quantum Monte Carlo (QMC) calculations to obtain benchmark QMC-KS potentials for a range of insulators and semiconductors, which we then compare to the KS potentials of popular density functional approximations (DFAs). Our results show that different DFAs yield similar electron densities, despite differences in their KS potentials, which originate primarily from the exchange and correlation contribution. We also find that the KS gap from the QMC density is typically larger than the KS gaps of most DFAs, with the exception of Hartree-Fock. Finally, the KS gap is sensitive to the inclusion of semicore states in the pseudopotentials, such that comparison with experiment should be done with caution.

Fermionic cold atoms in optical traps provide viable quantum simulators of correlation effects in electronic systems. For dressed Rydberg atoms in two-dimensional traps with out-of-plane dipole moments, a realistic model of the pairwise interaction is of repulsive dipolar 1 / r 3 form at long range, softened to a constant at short range. This study provides parametrizations of fixed-node diffusion Monte Carlo energy data for ferromagnetic (one-component) and paramagnetic (two-component) two-dimensional homogeneous Fermi fluids of interacting dipolar atoms. We find itinerant ferromagnetism to be unstable within our parameter spaces for dipolar interactions both with and without softening. Our parametrization of the energy as a function of density will enable density functional theory to support experimental studies of inhomogeneous fermionic cold-atom systems.

Dynamical response theory is employed to investigate the effects of various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths b and density parameters r s . In the regime of a thin quantum wire, electrons are treated as a one-dimensional gas under different confinement models via effective electron-electron interaction potentials. Using the first-order random phase approximation (FRPA) including self-energy and exchange contribution, which provides the ground-state structure beyond the random phase approximation, we numerically compute the structure factor, pair-correlation function, correlation energy, and ground-state energy for various values of b and r s . Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire ( b → 0 ) in the high-density limit, we find that the correlation energy for transverse confinement models V 1 ( q ) (harmonic), V 2 ( q ) (cylindrical), and V 5 ( q ) (harmonic-delta) approaches ε c ( r s ) = − π 2 / 360 ∼ − 0.02741 a.u., which agrees with the exact results in this limit [P.-F. Loos, ; V. Ashokan, , ]. This clearly illustrates that for at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance x = 0 to yield the same correlation energy. In contrast, other confinement potentials, V 3 ( q ) (infinite square well), V 4 ( q ) (infinite square-infinite triangular well), and V 6 ( q ) (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to ε c ∼ − 0.03002 a.u. for these potentials. The percentage difference in correlation energy between the confinement models V 1 ( q ) , V 2 ( q ) , V 5 ( q ) and V 3 ( q ) , V 4 ( q ) , V 6 ( q ) is within about 10 % in the high-density limit. The ground-state properties obtained from the FRPA are compared with the available quantum Monte Carlo results in the high-density regime. We observe that the peak height in the static structure factor at k = 2 k F depends significantly on the confinement model. These prominent peaks at k = 2 k F are fitted with a function based on our finite wire-width theory, guided by insights from bosonization, demonstrating good agreement with our FRPA theory.

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Furthermore, its excellent scalability with system complexity and near-perfect utilization of computational power make FN-DMC ideally positioned to leverage new advances in computing to address increasingly complex scientific problems. Even though the method is widely used as a computational gold standard, reproducibility across the numerous FN-DMC code implementations has yet to be demonstrated. This difficulty stems from the diverse array of DMC algorithms and trial wave functions, compounded by the method’s inherent stochastic nature. This study represents a community-wide effort to assess the reproducibility of the method, affirming that yes, FN-DMC is reproducible (when handled with care). Using the water–methane dimer as the canonical test case, we compare results from eleven different FN-DMC codes and show that the approximations to treat the non-locality of pseudopotentials are the primary source of the discrepancies between them. In particular, we demonstrate that, for the same choice of determinantal component in the trial wave function, reliable and reproducible predictions can be achieved by employing the T-move, the determinant locality approximation, or the determinant T-move schemes, while the older locality approximation leads to considerable variability in results. These findings demonstrate that, with appropriate choices of algorithmic details, fixed-node DMC is reproducible across diverse community codes—highlighting the maturity and robustness of the method as a tool for open and reliable computational science.

The real-space variation quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) are used to calculate the energy bands and the effective mass of the paramagnetic and ferromagnetic two-dimensional uniform electron liquid (2D-UEL). The many-body finite-size errors are minimized by performing simulations for three system sizes with the number of electrons, N = 146 , 218, and 302, for paramagnetic and N = 91 , 139, and 151 for ferromagnetic systems. We consider 2D-UEL to be within the density range 1 ≤ r s ≤ 10 . The VMC and DMC results predict that the effective mass m * of the paramagnetic 2D-UEL at high density r s = 1 is very close to 1, suggesting that the effective mass renormalization due to electron-electron interaction is negligible. We find that m * of the paramagnetic 2D-UEL obtained by the VMC and DMC methods increases by r s but with different slopes. Our VMC and DMC results for ferromagnetic 2D-UEL indicate that m * decreases rapidly by reducing the density due to the strong suppression of the electron-electron interaction.

We investigate interlayer adhesion and relaxation at interfaces between graphene and hexagonal boron nitride (hBN) monolayers in van der Waals heterostructures. The adhesion potential between graphene and hBN is calculated as a function of local lattice offset using diffusion quantum Monte Carlo methods, which provide an accurate treatment of van der Waals interactions. Combining the adhesion potential with elasticity theory, we determined the relaxed structures of graphene and hBN layers at interfaces, finding no metastable structures. The adhesion potential is well described by simple Lennard-Jones pair potentials that we parametrize using our quantum Monte Carlo data. Encapsulation of graphene between near-aligned crystals of hBN gives rise to a moiré pattern whose period is determined by the misalignment angle between the hBN crystals superimposed over the moiré superlattice previously studied in graphene on an hBN substrate. We model minibands in such supermoiré superlattices and find them to be sensitive to the 180° rotation of one of the encapsulating hBN crystals. We find that monolayer and bilayer graphene placed on a bulk hBN substrate and bulk hBN/graphene/bulk hBN systems do not relax to adopt a common lattice constant. The energetic balance is much closer for free-standing monolayer graphene/hBN bilayers and hBN/graphene/hBN trilayers. The layers in an alternating stack of graphene and hBN are predicted to strain to adopt a common lattice constant, and hence, we obtain a stable three-dimensional crystal with a distinct electronic structure.

We investigate interlayer adhesion and relaxation at interfaces between graphene and hexagonal boron nitride (hBN) monolayers in van der Waals heterostructures. The adhesion potential between graphene and hBN is calculated as a function of local lattice offset using diffusion quantum Monte Carlo methods, which provide an accurate treatment of van der Waals interactions. Combining the adhesion potential with elasticity theory, we determine the relaxed structures of graphene and hBN layers at interfaces, finding no metastable structures. The adhesion potential is well described by simple Lennard-Jones pair potentials that we parameterize using our quantum Monte Carlo data. Encapsulation of graphene between near-aligned crystals of hBN gives rise to a moiré pattern whose period is determined by the misalignment angle between the hBN crystals superimposed over the moiré superlattice previously studied in graphene on an hBN substrate. We model minibands in such supermoiré superlattices and find them to be sensitive to a 180$^\circ$ rotation of one of the encapsulating hBN crystals. We find that monolayer and bilayer graphene placed on a bulk hBN substrate and bulk hBN/graphene/bulk hBN systems do not relax to adopt a common lattice constant. The energetic balance is much closer for free-standing monolayer graphene/hBN bilayers and hBN/graphene/hBN trilayers. The layers in an alternating stack of graphene and hBN are predicted to strain to adopt a common lattice constant and hence we obtain a new, stable three-dimensional crystal with a unique electronic structure.

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 ≤ r s ≤ 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 ≤ r s ≤ 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. The DMC energies in the thermodynamic limit are used to parametrize 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 s = 35 ( 1 ) , with no region of stability for a ferromagnetic fluid. Published by the American Physical Society 2024