Variational Quantum Monte Carlo Approach Research Articles

Deep-neural-network approach to solving the ab initio nuclear structure problem

Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving condensed matter and chemistry problems, while for atomic nuclei it is still quite challenging because of the complicated nucleon-nucleon interactions, which strongly couple the spatial, spin, and isospin degrees of freedom. By combining essential physics of the nuclear wave functions and the strong expressive power of artificial neural networks, we develop FeynmanNet, a deep-learning variational quantum Monte Carlo approach for ab initio nuclear structure. We show that FeynmanNet can provide very accurate solutions of ground-state energies and wave functions for $^{4}\mathrm{He}, ^{6}\mathrm{Li}$, and even up to $^{16}\mathrm{O}$ as emerging from the leading-order and next-to-leading-order Hamiltonians of pionless effective field theory. Compared to the conventional diffusion Monte Carlo approaches, which suffer from the severe inherent fermion-sign problem, FeynmanNet reaches such a high accuracy in a variational way and scales polynomially with the number of nucleons. Therefore, it paves the way to a highly accurate and efficient ab initio method for predicting nuclear properties based on the realistic interactions between nucleons.

Response to “Comment on ‘The surplus function approach’ ” [J. Chem. Phys. 112, 455 (2000)

The existence of integral (Hi¯) in the surplus function variational quantum Monte Carlo approach is discussed and a method is proposed for avoiding the infinity in the calculation of Hi¯. A rigid model of nucleus was adopted to avoid the infinity appearance of r−i. Discussion of a new solution for Schrödinger’s equation of hydrogen atom, which may make the calculation of the Hi¯ value more accurate is also presented.

Surplus function variational quantum Monte Carlo approach: Excited state processing

Surplus function variational quantum Monte Carlo approach used for the excited state of electrons has been proposed. If the initial wave functions of both the excited state and ground state belong to the irreducible representation with different symmetries, the surplus function variational quantum Monte Carlo approach of the excited state is identical to that of the ground state, and if they belong to the irreducible representation with an identical symmetry, the surplus function variational quantum Monte Carlo approach of the ground state can also be applied to the excited state only by orthogonal revision for the initial wave function of the excited state. The detailed calculations formulas on the surplus function variational quantum Monte Carlo approach of the excited state have been deduced. A complete set of the surplus function variational quantum Monte Carlo approach for both the ground state and excited state has been established. The energy values of X 3B1, 1 1A1, and 2 1A1 states of CH2 have been calculated using this approach. The calculation results show that the precision of the surplus function variational quantum Monte Carlo approach is comparable to that of FCI approach only by iteration to the third-order energy value for three states of CH2. The correlation energy percentages of the fourth- and the fifth-order energy obtained by the surplus function variational quantum Monte Carlo approach are over 80% and 90%, respectively. This indicates that the approach is successful both in the ground state and in the excited state.

Variational quantum Monte Carlo calculation of the cohesive properties of cubic boron nitride

The cohesive properties of cubic boron nitride are calculated using the variational quantum Monte Carlo approach. The calculated properties are found to be in good agreement with experiment and demonstrate the effectiveness of the variational forms of wave functions previously used in $\mathrm{sp}$-bonded systems involving only one chemical species when applied to solids with more than one type of atom. The formulation of variance minimization for the one-body term in solids without inversion symmetry is presented, and a particularly simple form of one-body term based on a charge-fluctuation picture of electron correlation is shown to obtain excellent results for ground-state energies of B, C, and N atoms, and for the cubic boron nitride solid.

Pseudopotential variational quantum Monte Carlo approach to bcc lithium.

The pseudopotential variational quantum Monte Carlo scheme is applied to bcc lithium. The pseudopotential is constructed from all-electron Hartree-Fock calculations. Atomic levels calculated using the pseudopotential show good agreement with experimental atomic spectroscopic data. Calculations for bcc lithium provide accurate equilibrium lattice constant and bulk modulus. Calculated cohesive energy is within 0.1 eV of the experimental value. Use of the pseudopotential enables accurate evaluation of the correlation energy among the conduction electrons. The results have demonstrated that the correlation energy is very important in determining bulk lithium properties. \textcopyright{} 1996 The American Physical Society.

Variational Quantum Monte Carlo Approach to the Electronic Structure of NiO

The electronic structure of NiO solid with the fcc type-II antiferromagnetic structure has been studied using a variational quantum Monte Carlo approach. The Jastrow-Slater many-body wave function has been used for valence electrons, and the pseudopotentials have been evaluated with the aid of a local approximation. The calculated results for the binding energy and the structural properties are in good agreement with experiment. Reasonable evaluations have also been made for the charge and spin density distributions and the electron-electron radial distribution functions. Although the results for the one-particle energy distribution and the charge-transfer excitation energy gap are encouraging, further increase in Monte Carlo steps and improvements in computational methods would be required for the detailed comparison with experiments and the most dependable density-functional band calculations.

Theory of the spin-flip excitations in the nu =1 quantum Hall liquid.

We calculated the spin-gap enhancement in the \ensuremath{\nu}=1 quantum Hall liquid using a variational quantum Monte Carlo approach. The approach goes beyond the usual lowest-Landau-level approximation. A significant (\ensuremath{\sim}50% at ${\mathit{r}}_{\mathit{s}}$=2) reduction in the single spin-flip gap due to Landau-level mixing is found for typical experimental situations. Final-state effects and the finite thickness of the electron gas are conveniently included in our formalism, and satisfactorily explain recent photoluminescence experiments on \ensuremath{\delta}-doped samples.

Spiral states in the three-band Hubbard model: A Hartree-Fock and variational quantum Monte Carlo approach.

Two methods are used, Hartree-Fock and a variational wave function, to investigate spiral states in the three-band Hubbard model. Our variational wave function is a Gutzwiller-projected Hartree-Fock spiral state. We use quantum Monte Carlo methods to calculate the variational energy exactly. In order to avoid boundary defects in the spiral spin structure, we work in a frame where the spin-quantization axis is locally rotated. Both methods show that upon doping the antiferromagnetic structure present at half-band-filling is unstable against a (1,1) spiral state

Erratum: Variational quantum Monte Carlo nonlocal pseudopotential approach to solids: Formulation and application to diamond, graphite, and silicon

A new method of calculating total energies of solids and atoms using nonlocal pseudopotentials in conjunction with the variational quantum Monte Carlo approach is presented in detail. The many-electron wave function is of the form of a Jastrow exponential factor multiplying a Slater determinant. By using pseudopotentials, the large fluctuations of the energies in the core region of the atoms which occur in quantum Monte Carlo all-electron calculations are avoided. The method is applied to calculate the binding energy and structural properties of diamond, graphite, and silicon. The results are in excellent agreement with experiment. Excellent results are also obtained for the electron affinities and ionization potentials of the carbon and silicon atoms.

Magnetic structure and equation of state of bcc solid hydrogen: A variational quantum Monte Carlo study.

Solid hydrogen in the atomic bcc structure is studied using a variational quantum Monte Carlo approach. Various magnetic phases are investigated at densities between Wigner-Seitz radius of ${\mathit{r}}_{\mathit{s}}$=1.6 and 3.0 a.u. Correlated wave functions of Jastrow-Slater form are used with their antisymmetric part constructed from the Kohn-Sham self-consistent orbitals. A transition from paramagnetic to antiferromagnetic phase at lower density is found at ${\mathit{r}}_{\mathit{s}}$=2.4. There is, however, no evidence for metastable partial ferromagnetic structure.

Pair-correlation function and single-particle occupation numbers in diamond and silicon.

The electron pair-correlation function for diamond is calculated using a variational quantum Monte Carlo approach. The full pair-correlation function reveals striking anisotropy and spatial-dependent structures that result from the crystal structure and chemical bonding of the real material. The effects of correlation on the occupation of single-particle states have also been calculated for diamond and silicon, as well as quasihole energies within a single-mode approximation.

Variational quantum Monte Carlo nonlocal pseudopotential approach to solids: Cohesive and structural properties of diamond.

A new method of calculating total energies of solids using nonlocal pseudopotentials in conjunction with the variational quantum Monte Carlo approach is presented. By use of pseudopotentials, the large fluctuations of the energies in the core region of the atoms which occur in quantum Monte Carlo all-electron calculations are avoided. The method is applied to calculate the binding energy and structural properties of diamond. The results are in excellent agreement with experiment.

Variational Quantum Monte Carlo Calculation of Materials Properties

AbstractA new method of calculating the total energy and other ground-state properties of solids which employs nonlocal pseudopotentials in conjunction with the variational quantum Monte Carlo approach is presented. Valence electron correlations are treated using the exact interaction with a correlated many-electron wavefunction of the Jastrow-Slater form. The use of pseudopotentials for the electron-ion interaction removes from the problem the large fluctuations of electron energies in the core region which occur in quantum Monte Carlo all-electron schemes. We discuss calculation of the cohesive energy and structural properties of diamond and graphite and the ionization energy and electron affinity of atoms using the present approach. The results are in excellent agreement with experiment.