Variational Monte Carlo Calculations Research Articles

Spin-12HeisenbergJ1−J2antiferromagnet on the kagome lattice

We report variational Monte Carlo calculations for the spin-$\frac{1}{2}$ Heisenberg model on the kagome lattice in the presence of both nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic superexchange couplings. Our approach is based upon Gutzwiller projected fermionic states that represent a flexible tool to describe quantum spin liquids with different properties (e.g., gapless and gapped). We show that, on finite clusters, a gapped $\mathbb{Z}_{2}$ spin liquid can be stabilized in the presence of a finite $J_2$ superexchange, with a substantial energy gain with respect to the gapless $U(1)$ Dirac spin liquid. However, this energy gain vanishes in the thermodynamic limit, implying that, at least within this approach, the $U(1)$ Dirac spin liquid remains stable in a relatively large region of the phase diagram. For $J_2/J_1 \gtrsim 0.3$, we find that a magnetically ordered state with ${\bf q}={\bf 0}$ overcomes the magnetically disordered wave functions, suggesting the end of the putative gapless spin-liquid phase.

Variational Study on Loop Currents in Bose Hubbard model with Staggered Flux

In view of strongly interacting bosons in an optical lattice with a large gauge field, we study phase transitions in a two-dimensional Bose-Hubbard model with a staggered flux, on the basis of variational Monte Carlo calculations. Inthe trial states,besides typical onsite and intersite correlation factors, we introduce a configuration-dependent phase factor,which was recently found essential for treating current-carrying states. It is found that this phase factor is qualitativelyvitalfordescribing a Mott insulating (MI) state in the present model. Thereby, the Peierls phasesattached in relevant hopping processes are cancelled out. As a result, local currents completely suppressed in MI states, namely, a chiral Mott state does not appear for the square lattice, in contrast tothecorresponding two-leg ladder model. In addition, we discuss other features of the first-order superfluid-MI transition in this model.

Auxiliary-field quantum Monte Carlo simulations of neutron matter in chiral effective field theory.

We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wave function of neutron matter, containing nonperturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10(3) discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of Λ=414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt Λ=414 MeV [L. Coraggio et al., Phys. Rev. C 87, 014322 (2013).

Origin of high-Tcsuperconductivity in doped Hubbard models and their extensions: Roles of uniform charge fluctuations

Doped Hubbard model is a simple model for the high-Tc cuprate superconductors, while its ground state remains a challenge. Here, by performing state-of-the-art variational Monte Carlo calculations for the strong-coupling Hubbard model, we find evidences that the d-wave superconducting phase emerges always near the phase separation region and the superconducting order has one-to-one correspondence with the enhancement of charge compressibility. The order as well as the phase separation are vulnerable to realistic intersite Coulomb interaction while the superexchange interaction enhances both. An appropriate combination of these two widens the stable superconducting phase.

Importance of high-angular-momentum channels in pseudopotentials for quantum Monte Carlo

Quantum Monte Carlo methods provide in principle a highly accurate treatment of the many-body problem of calculating the ground and excited states of condensed systems. In practice, however, uncontrolled errors, such as those arising from the fixed-node and pseudopotential approximations can be problematic. We show that the accuracy of some quantum Monte Carlo calculations is limited by the properties of currently available pseudopotentials. The use of pseudopotentials involves several approximations, and we will focus on one that is relatively simple to correct during the pseudopotential design phase. It is necessary to include angular-momentum channels in the pseudopotential for excited angular-momentum states and to choose the local channel appropriately to obtain accurate results. Variational and diffusion Monte Carlo calculations for Zn, O, and Si atoms and ions demonstrate these issues. Adding higher-angular-momentum channels into the pseudopotential description reduces such errors without a significant increase in computational cost.

Fermionic superfluid from a bilayer band insulator in an optical lattice

We propose a model to realize a fermionic superfluid state in an optical lattice circumventing the cooling problem. Our proposal exploits the idea of tuning the interaction in a characteristically low entropy state, a band-insulator in an optical bilayer system, to obtain a superfluid. By performing a detailed analysis of the model including fluctuations and augmented by a variational quantum Monte Carlo calculations of the ground state, we show that the superfluid state obtained has high transition temperature of the order of the hopping energy. Our system is designed to suppress other competing orders such as a charge density wave. We suggest a laboratory realization of this model via an orthogonally shaken optical lattice bilayer.

Auxiliary-field quantum Monte Carlo simulations of neutron matter in chiral effective field theory

We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear interactions. The ground-state wavefunction of neutron matter, containing nonperturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10 discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin-independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of chiral nuclear forces. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of 414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction are then treated perturbatively. Our results for the equation of state are compared to previous quantum Monte Carlo simulations which employed chiral two-body forces at next-to-next-to-leading order (N2LO). In addition we include the effects of three-body forces at N2LO, which provide important repulsion at densities higher than 0.02 fm, as well as two-body forces at N3LO.

Phase Diagram of a Three-Orbital Model for High-TcCuprate Superconductors

We study the phase diagram of an effective three-orbital model of the cuprates using variational MonteCarlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.

Nucleon and nucleon-pair momentum distributions inA≤12nuclei

We report variational Monte Carlo calculations of single-nucleon momentum distributions for A <= 12 nuclei and nucleon-pair and nucleon-cluster momentum distributions for A <= 8. The wave functions have been generated for a Hamiltonian containing the Argonne v18 two-nucleon and Urbana X three-nucleon potentials. The single-nucleon and nucleon-pair momentum distributions exhibit universal features attributable to the one-pion-exchange tensor interaction. The single-nucleon distributions are broken down into proton and neutron components and spin-up and spin-down components where appropriate. The nucleon-pair momentum distributions are given separately for pp and pn pairs. The nucleon-cluster momentum distributions include dp in 3He, tp and dd in 4He, alpha-d in 6Li, alpha-t in 7Li, and alpha-alpha in 8Be. Detailed tables are provided on-line for download.

Ab Initio Geometry and Bright Excitation of Carotenoids: Quantum Monte Carlo and Many Body Green's Function Theory Calculations on Peridinin.

In this letter, we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) Å, larger than the values obtained by DFT (PBE, B3LYP, and CAM-B3LYP) and shorter than that calculated at the Hartree-Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO-LUMO major contribution of the Bu(+)-like (S2) bright excited state. Many Body Green's Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu(+)-like state for the VMC structure (VMC/MBGFT) provide an excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed.

Scaling in the correlation energies of two-dimensional artificial atoms

We find an unexpected scaling in the correlation energy of artificial atoms, i.e., harmonically confined two-dimensional quantum dots. The scaling relation is found through extensive numerical examinations including Hartree–Fock, variational quantum Monte Carlo, density functional, and full configuration interaction calculations. We show that the correlation energy, i.e., the true ground-state total energy minus the Hartree–Fock total energy, follows a simple function of the Coulomb energy, confinement strength and number of electrons. We find an analytic expression for this function, as well as for the correlation energy per particle and for the ratio between the correlation and total energies. Our tests for independent diffusion Monte Carlo and coupled-cluster results for quantum dots—including open-shell data—confirm the generality of the scaling obtained. As the scaling also applies well to ≳100 electrons, our results give interesting prospects for the development of correlation functionals within density functional theory.

Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule.

Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.

4He clusters adsorbed on graphene

We report the results of a study of ${}^{4}$He${}_{N}$ clusters, for $2\ensuremath{\le}N\ensuremath{\le}40$, adsorbed on one and both sides of a graphene sheet. The ground-state properties are determined using variational and diffusion Monte Carlo calculations at zero temperature, and in addition path integral Monte Carlo simulations at finite temperature are performed for some selected cluster sizes. For the interaction of helium atoms with graphene, we compare several models: a smooth He-graphene potential that depends only on the distance to the graphene sheet and potentials constructed as a sum of individual He-C interactions where two possibilities for this He-C interaction are tested. In this way, we assess the effect of corrugation on the binding properties of helium clusters. Furthermore, we study the influence that the graphene-mediated McLachlan dispersion energy has on the He-He interaction. The McLachlan interaction weakens the attraction between helium atoms, which turns out to have a significant effect on the binding energy and the shape of adsorbed ${}^{4}$He clusters. We find that clusters adsorbed on opposite sides of graphene are bound, but according to the He-He pair distribution function across the graphene sheet, pair correlations are very weak. For a large enough number of particles, solidlike $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structures start to become energetically preferred for the model of anisotropic corrugation without the McLachlan interaction. For the other models, the ground state of the studied clusters is clearly liquidlike.

Correlation Consistent Gaussian Basis Sets for H, B-Ne with Dirac-Fock AREP Pseudopotentials: Applications in Quantum Monte Carlo Calculations.

In this paper, we introduce correlation consistent Gaussian-type orbital basis sets for the H and B-Ne atoms for use with the CASINO Dirac-Fock AREP pseudopotentials. These basis sets are tested in coupled cluster calculations on H2, B2, C2, N2, O2, and F2 as well as in quantum Monte Carlo calculations on the water monomer and dimer and the water-benzene complex, where they are found to give low variances in variational Monte Carlo calculations and to lead to reduced time step errors and improved convergence in diffusion Monte Carlo calculations compared to the use of nonoptimized basis sets. The use of basis sets with a large number of contracted s and p primitives is found to be especially important for the convergence of the energy in the diffusion Monte Carlo calculations.

Variational Monte Carlo Study of ΛΛ4H

Variational Monte Carlo calculations are carried out for ΛΛ4H to explore the possibility of its existence, using realistic NN, NNN, and phenomenological ΛN and ΛNN interactions. We also perform calculations using FGNN and NSC97 ΛN potentials, and demonstrate the effect of the exchange part of the two-body ΛN interaction and three-body ΛNN interaction on the binding energy of ΛΛ4H. Still the stability of ΛΛ4H remains an open question and this hypernuclear system has to be explored more theoretically.

Sensory-organ-like response determines the magnetism of zigzag-edged honeycomb nanoribbons

We present an analytical effective theory for the magnetic phase diagram for zigzag-edge terminated honeycomb nanoribbons described by a Hubbard model with an interaction parameter $U$. We show that the edge magnetic moment varies as $\mathrm{ln}U$ and uncover its dependence on the width $W$ of the ribbon. The physics of this owes its origin to the sensory-organ-like response of the nanoribbons, demonstrating that considerations beyond the usual Stoner-Landau theory are necessary to understand the magnetism of these systems. A first-order magnetic transition from an antiparallel orientation of the moments on opposite edges to a parallel orientation occurs upon doping with holes or electrons. The critical doping for this transition is shown to depend inversely on the width of the ribbon. Using variational Monte Carlo calculations, we show that magnetism is robust to fluctuations. Additionally, we show that the magnetic phase diagram is generic to zigzag-edge terminated nanostructures such as nanodots. Furthermore, we perform first-principles modeling to show how such magnetic transitions can be realized in substituted graphene nanoribbons.

Correlated-Electron Systems and High-Temperature Superconductivity

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlo method. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa_2Cu_3O_7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. The relationship of the hole density x and incommensurability \delta, \delta\sim x, is satisfied in the lower doping region, as indicated by the variational Monte Carlo calculations. We have performed a variational Monte Carlo simulation on a two-dimensional t-t'-t"-U Hubbard model with a Bi-2212 type band structure and found that the 4\times 4 period checkerboard spin modulation, that is characterized by multi Q vectors, is stabilized. We also present a new algorithm of the diagonalization quantum Monte Carlo method that is a method for the evaluation of expectation values without the negative sign difficulty. We show that the pair correlation function is not enhanced at half-filling, and is indeed enhanced with hole doping.

Reaction pathways by quantum Monte Carlo: insight on the torsion barrier of 1,3-butadiene, and the conrotatory ring opening of cyclobutene.

Quantum Monte Carlo (QMC) methods are used to investigate the intramolecular reaction pathways of 1,3-butadiene. The ground state geometries of the three conformers s-trans, s-cis, and gauche, as well as the cyclobutene structure are fully optimised at the variational Monte Carlo (VMC) level, obtaining an excellent agreement with the experimental results and other quantum chemistry high level calculations. Transition state geometries are also estimated at the VMC level for the s-trans to gauche torsion barrier of 1,3-butadiene and for the conrotatory ring opening of cyclobutene to the gauche-1,3-butadiene conformer. The energies of the conformers and the reaction barriers are calculated at both variational and diffusional Monte Carlo levels providing a precise picture of the potential energy surface of 1,3-butadiene and supporting one of the two model profiles recently obtained by Raman spectroscopy [Boopalachandran et al., J. Phys. Chem. A 115, 8920 (2011)]. Considering the good scaling of QMC techniques with the system's size, our results also demonstrate how variational Monte Carlo calculations can be applied in the future to properly investigate the reaction pathways of large and correlated molecular systems.

Optimized Structure and Vibrational Properties by Error Affected Potential Energy Surfaces

The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work, we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies, and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the statistical uncertainty of the vibrational parameters by 1 order of magnitude. Preliminary results based on variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters and harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties).

Mott Transition and Phase Diagram of κ-(BEDT-TTF)2Cu(NCS)2Studied by Two-Dimensional Model Derived fromAb initioMethod

We present an ab initio analysis for the ground-state properties of a correlated organic compound $\kappa$-(BEDT-TTF)2Cu(NCS)2. First, we derive an effective two-dimensional low-energy model from first principles, having short-ranged transfers and short-ranged Coulomb and exchange interactions. Then, we perform many-variable variational Monte Carlo calculations for this model and draw a ground-state phase diagram as functions of scaling parameters for the onsite and off-site interactions. The phase diagram consists of three phases; a paramagnetic metallic phase, an antiferromagnetic (Mott) insulating phase, and a charge-ordered insulating phase. In the phase diagram, the parameters for the real compound are close to the first-order Mott transition, being consistent with experiments. We show that the off-site Coulomb and exchange interactions affect the phase boundary; (i) they appreciably stabilize the metallic state against the Mott insulating phase and (ii) enhance charge fluctuations in a wide parameter region in the metallic phase. We observe arc-like structure in Fermi surface around the region where the charge fluctuations are enhanced. Possible relevance of the charge fluctuations to the experimentally observed dielectric anomaly in the $\kappa$-BEDT-TTF family compounds is also pointed out.