Variational Monte Carlo Calculations Research Articles

Inhomogeneous state of the extendedt-Jmodel on a square lattice: A variational Monte Carlo and Gutzwiller approximation study

We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density, and pair field, of the mean-field ground state of the $t$-$J$ model. It leads to the stripe patterns we have found numerically in a generalized $t$-$J$-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust $d$-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the ``in-phase'' magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.

Structural Optimization by Quantum Monte Carlo: Investigating the Low-Lying Excited States of Ethylene.

We present full structural optimizations of the ground state and of the low lying triplet state of the ethylene molecule by means of Quantum Monte Carlo methods. Using the efficient structural optimization method based on renormalization techniques and on adjoint differentiation algorithms recently proposed [Sorella, S.; Capriotti, L. J. Chem. Phys.2010, 133, 234111], we present the variational convergence of both wave function parameters and atomic positions. All of the calculations were done using an accurate and compact wave function based on Pauling's resonating valence bond representation: the Jastrow Antisymmetrized Geminal Power (JAGP). All structural and wave function parameters are optimized, including coefficients and exponents of the Gaussian primitives of the AGP and the Jastrow atomic orbitals. Bond lengths and bond angles are calculated with a statistical error of about 0.1% and are in good agreement with the available experimental data. The Variational and Diffusion Monte Carlo calculations estimate vertical and adiabatic excitation energies in the ranges 4.623(10)-4.688(5) eV and 3.001(5)-3.091(5) eV, respectively. The adiabatic gap, which is in line with other correlated quantum chemistry methods, is slightly higher than the value estimated by recent photodissociation experiments. Our results demonstrate how Quantum Monte Carlo calculations have become a promising and computationally affordable tool for the structural optimization of correlated molecular systems.

Comparative study of three-nucleon potentials in nuclear matter

A new generation of local three-body potentials providing an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length, has been recently derived. We have performed a comparative analysis of the equations of state of both pure neutron matter (PNM) and symmetric nuclear matter (SNM) at zero temperature obtained using these models of three-nucleon forces. In particular, we have carried out both variational and auxiliary field diffusion Monte Carlo calculations of the equation of state of PNM, while in the case of SNM we have only the variational approach has been considered. None of the considered potentials simultaneously explains the empirical equilibrium density and binding energy of symmetric nuclear matter. However, two of them provide reasonable values of the saturation density. The ambiguity concerning the treatment of the contact term of the chiral inspired potentials is discussed.

Adsorption of 4He N and 4He N 3He Clusters on Cesium

The ground-state properties of helium clusters 4He N and 4He N 3He, for N≤ 40, adsorbed on the surface of cesium are studied using variational and diffusion Monte Carlo calculations. Binding properties are determined using two different Cs–He interaction potentials. For the smallest clusters, self-binding on a Cs surface is stronger than in two or three dimensions. For N > 10 self-binding in three dimensions is stronger than on Cs for both types of Cs–He interaction potential considered. The obtained binding energies and structure are compared to results of recent density functional calculations. The emergence of edge states of 3He atom, localized along the contact line of 4He cluster with a cesium surface, is studied. First indication that 3He atom prefers to be close to the contact line appears already for the 4He3 3He cluster.

Complete optimisation of multi-configuration Jastrow wave functions by variational transcorrelated method

We investigate the performance of the newly developed variational transcorrelated (VTC) method (H. Luo, J. Chem. Phys. 133, 154109 (2010)) on the overall optimisation of the multi-configuration Jastrow wave function. Similar to the standard multi-configuration self consistent field methods, optimisations of orbitals are realized by iterative unitary transformations, where the skew-symmetric matrix elements are determined by using Newton-Raphson scheme. Third order density matrices are introduced to deal with the three-body VTC potential. Test calculations are performed for the C(2) molecule on several small complete active spaces, and the results are compared with those of variational quantum Monte Carlo calculations. The results demonstrate that with the VTC method one can practically recover the results of highly non-linear variational calculations.

Determining a Skyrme-type effective interaction from realistic two-nucleon interaction

The Variational Monte Carlo (VMC) method is employed to determine characteristics of symmetric and asymmetric nuclearmatter. The realistic Urbana v14 nucleon-nucleon interaction potential of Lagaris and Pandharipande was used in the VMC calculations with addition of a phenomenological density-dependent term to simulate many-body interactions. A new Skyrme parameter set SKaan-U14 is found to consistently reproduce the characteristics of the nuclear matter obtained from VMC calculations. The properties of symmetric and asymmetric nuclear matter are calculated by the new Skyrme parameter set. The results obtained by using the new Skyrme parameter set are compared with results obtained by different Skyrme parameter sets in the literature.

Mott physics on helical edges of two-dimensional topological insulators

We study roles of electron correlations on topological insulators or quantum spin Hall insulators on honeycomb lattice with spin-orbit interaction. Accurate variational Monte Carlo calculations with a large number of variational parameters show that the increasing on-site Coulomb interactions cause a strong suppression of the charge Drude weight in the helical-edge metallic states leading to a presumable Mott transition (or strong crossover) from a conventional topological insulator to an edge Mott insulator before a transition to a bulk antiferromagnetic insulator. The intermediate bulk-topological and edge-Mott-insulator phase has a helical spin-liquid character with time-reversal symmetry.

Jastrow correlated and quantum Monte Carlo calculations for the low-lying states of the carbon atom

Different computational methods are employed to calculate excitation energies of the carbon atom. Explicitly correlated wave functions have been obtained in a Variational Monte Carlo calculation. Fixed node Diffusion Monte Carlo calculations for the lowest energy excited states of a given symmetry are reported. A systematic and quantitative analysis of the performance of the different schemes in the calculation of the excitation energy of up to 27 excited states of the carbon atom is carried out. The quality of the different methods have been studied in terms of the deviation with respect to the experimental excitation energies. A good agreement with the experimental values has been reached.

On the Lindemann Criterion for Quantum Clusters at Very Low Temperature

The Lindemann criterion to discern the solid-like or liquid-like nature of a quantum cluster at T = 0 is discussed. A critical analysis of current Lindemann parameters is presented and a new parameter is proposed that is appropriate to study quantum clusters made of identical particles. A simple model wave function is introduced to fix the range of variation of these parameters. The model presents two extreme limits that correspond to either a liquid-like or a solid-like system; besides, it fulfills the Bose symmetry and also permits evaluations without symmetrization. Variational and diffusion Monte Carlo calculations are also performed for clusters of spinless bosons interacting through Lennard-Jones potentials. It is shown that the liquid-like or solid-like character of quantum clusters at zero temperature cannot be simply established in terms of a single parameter.

Exotic Gapless Mott Insulators of Bosons on Multileg Ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.

Variational transcorrelated method

We propose a new approach to the use of Jastrow ansatz in the calculation of electron correlations, based on a modification of the transcorrelated method of Boys and Handy [Proc. R. Soc. London, Ser. A 309, 209 (1969)]. In this new method, the original transcorrelated orbital equation is replaced with a general variational equation for the reference wave function, whereas the equation for the correlation factor remains the same. The method can be applied to a single determinant Jastrow ansatz as well as to a multideterminant one. For the single determinant ansatz, we obtain a Hartree-Fock type self-consistent equation for the optimization of orbitals, and for the multideterminant ansatz we have tested a CI type equation. We apply the new method in calculations of the C(2) molecule and compare the results with those of variational quantum Monte Carlo calculations.

Variational quantum monte carlo calculation of the ground state energy of hydrogen molecule

Variational quantum monte carlo calculation of the ground state energy of hydrogen molecule

Fractional quantum Hall states in the vicinity of Mott plateaus

We perform variational Monte-Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one-another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground-state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.

Ultracold atoms at unitarity within quantum Monte Carlo methods

Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. The ratio of the energy of the interacting to the non-interacting gas for a system of 128 particles is calculated to be 0.4517(3) in VMC and 0.4339(1) in the more accurate DMC method. The spherically-averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, but the two-body density matrices and condensate fractions show some differences. Our best estimate of the condensate fraction of 0.51 is a little smaller than values from other quantum Monte Carlo calculations.

Relativistic quantum Monte Carlo method using zeroth-order regular approximation Hamiltonian

We propose a new relativistic treatment in the quantum Monte Carlo (QMC) technique using the zeroth-order regular approximation (ZORA) Hamiltonian. The novel ZORA local energy is derived, and its availability is examined with some variational Monte Carlo calculations. We optimize the wave functions variationally and evaluate the relativistic and correlation effects simultaneously. It is shown that our ZORA-QMC method with Jastrow-Slater wave functions can recover not only relativistic effects but also almost the same amount of electron correlations as the nonrelativistic QMC method can by evaluating the ionization potentials of the first row atoms, Li-Ne.

Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules

We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.

Near Degeneracy Effects on the Low-Lying Spectrum of the Iron Atom

The ground state and the LS terms coming from the ground-state configuration, [Ar]-3d(6)4s(2), of the iron atom are studied by carrying out an all electron Variational Monte Carlo calculation. Explicitly correlated trial functions including near degeneracy effects are used. The effect of electronic correlations and the importance of near degeneracy effects are systematically analyzed for the states here considered and compared with the experimental values. Correlations are important to reproduce, even qualitatively, the low-lying spectrum of this atom. A significant quantitative improvement when comparing with the experimental values is achieved when near degeneracy is considered along with dynamic correlations in the variational trial wave function. Finally, the effect of relativity on the results here reported is discussed.

Phase diagram for a t-J bilayer: role of interlayer couplings

The phase diagram for a t-J bilayer as a function of interplanar hopping, t⊥ and hole concentration, x is presented for a few different values of interplanar exchange, J⊥ using variational Monte Carlo calculations. The phase diagram shows rich features, such as a coexistence of antiferromagnetism and superconductivity at underdoping, planar (d-wave) and interplanar (dz-wave) superconducting correlations for small and large J⊥, respectively at optimal and overdoping. Another unusual feature appears in the form of a dome shaped structure in the phase diagram where the superconducting correlations are initially assisted as interplanar hopping is enhanced for small t⊥, while larger t⊥ is found to be detrimental to superconductivity.

Nature and Strength of Interlayer Binding in Graphite

We compute the interlayer bonding properties of graphite using an ab initio many-body theory. We carry out variational and diffusion quantum Monte Carlo calculations and find an equilibrium interlayer binding energy in good agreement with most recent experiments. We also analyze the behavior of the total energy as a function of interlayer separation at large distances comparing the results with the predictions of the random phase approximation.

Coexistence between checkerboarded charge and striped spin in two-dimensional Hubbard model

We have performed a variational Monte Carlo (VMC) simulation on a two-dimensional t–t′–t″–U Hubbard model to examine the stability of a 4×4 checkerboard state, which has been observed recently by scanning tunneling microscopy (STM) in Bi2Sr2CaCu2O8−δ and Ca2−xNaxCuO2Cl2 (Na–CCOC). In our VMC calculation, the checkerboard mean field wave function for the coexisting checkerboarded charge density wave in a striped spin density wave was used. We chose the transfer energies t′ and t″ suitable for Bi-based cuprate at the underdoping. The variational energy of the checkerboard state with 4×4 period comparable with that of the 4-period stripe state was obtained. It is important for stabilization of the checkerboard state that a Fermi surface around each of k=(π,0) and (0,π) points consists of two parallel flat section.