arXiv subjects

Shiwei Zhang

Publications and source records attributed to Shiwei Zhang.

At least 199 records · Page 11Linked to original sources

arXiv2016

Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix

Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem. The constraint involves an input trial wave function which restricts the random walks. We introduce a systematically improvable constraint which relies on the fundamental role of the density or one-body density matrix. An independent-particle calculation is coupled to an auxiliary-field QMC calculation. The independent-particle solution is used as the constraint in QMC, which then produces the input density or density matrix for the next iteration. The constraint is optimized by the self-consistency between the many-body and independent-particle calculations. The approach is demonstrated in the two-dimensional Hubbard model by accurately determining the ground state when collective modes separated by tiny energy scales are present in the magnetic and charge correlations. Our approach also provides an ab initio way to predict effective interaction parameters for independent-particle calculations.

cond-mat.str-el↗

arXiv2016

Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space

We describe the computational ingredients for an approach to treat interacting fermion systems in the presence of pairing fields, based on path-integrals in the space of Hartree-Fock-Bogoliubov (HFB) wave functions. The path-integrals can be evaluated by Monte Carlo, via random walks of HFB wave functions whose orbitals evolve stochastically. The approach combines the advantage of HFB theory in paired fermion systems and many-body quantum Monte Carlo (QMC) techniques. The properties of HFB states, written in the form of either product states or Thouless states, are discussed. The states are shown to be propagated by generalized one-body operators. The states can be stabilized for numerical iteration, and overlaps between two such states and one-body Green's functions can be computed. A constrained-path or phaseless approximation can be applied to the random walks of the HFB states if a sign problem or phase problem is present. The method is illustrated with an exact numerical projection in the Kitaev model, and in the Hubbard model with attractive interaction under an external pairing field.

cond-mat.str-el↗

arXiv2016

Efficient Web-based Data Imputation with Graph Model

A challenge for data imputation is the lack of knowledge. In this paper, we attempt to address this challenge by involving extra knowledge from web. To achieve high-performance web-based imputation, we use the dependency, i.e.FDs and CFDs, to impute as many as possible values automatically and fill in the other missing values with the minimal access of web, whose cost is relatively large. To make sufficient use of dependencies, We model the dependency set on the data as a graph and perform automatical imputation and keywords generation for web-based imputation based on such graph model. With the generated keywords, we design two algorithms to extract values for imputation from the search results. Extensive experimental results based on real-world data collections show that the proposed approach could impute missing values efficiently and effectively compared to existing approach.

cs.DB↗

arXiv2016

Auxiliary-field quantum Monte Carlo calculations with multiple-projector pseudopotentials

We have implemented recently developed multiple-projector pseudopotentials into the planewave based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. Multiple-projector pseudopotentials can yield smaller planewave cut-offs while maintaining or improving transferability. This reduces the computational cost of pw-AFQMC, increasing its reach to larger and more complicated systems. We discuss the use of non-local pseudopotentials in the separable Kleinman-Bylander form, and the implementation in pw-AFQMC of the multiple-projector optimized norm-conserving pseudopotential ONCVPSP of Hamann. The accuracy of the method is first demonstrated by equation-of-state calculations of the ionic insulator NaCl and more strongly correlated metal Cu. The method is then applied to calibrate the accuracy of density functional theory (DFT) predictions of the phase stability of recently discovered high temperature and pressure superconducting sulfur hydride systems. We find that DFT results are in good agreement with pw-AFQMC, due to near cancellation of electron-electron correlation effects between different structures.

cond-mat.mtrl-sci↗

arXiv2016

Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte Carlo

We address the calculation of dynamical correlation functions for many fermion systems at zero temperature, using the auxiliary-field quantum Monte Carlo method. The two-dimensional Hubbard hamiltonian is used as a model system. Although most of the calculations performed here are for cases where the sign problem is absent, the discussions are kept general for applications to physical problems when the sign problem does arise. We study the use of twisted boundary conditions to improve the extrapolation of the results to the thermodynamic limit. A strategy is proposed to drastically reduce finite size effects relying on a minimization among the twist angles. This approach is demonstrated by computing the charge gap at half-filling. We obtain accurate results showing the scaling of the gap with the interaction strength $U$, connecting to the scaling of the unrestricted Hartree-Fock method at small $U$ and Bethe Ansatz exact result in one dimension at large $U$. A new algorithm is then proposed to compute dynamical Green functions and correlation functions which explicitly varies the number of particles during the random walks in the manifold of Slater determinants. In dilute systems, such as ultracold Fermi gases, this algorithm enables calculations with much more favorable complexity, with computational cost proportional to basis size or the number of lattice sites.

cond-mat.str-el↗

arXiv2016

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver

We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo (AFQMC) impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA- DMET exhibits faster asymptotic convergence towards the thermodynamic limit (TDL). We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U/t = 2, 4, 6. These results compare favourably with the best data available in literature, and help resolve earlier uncertainties in the moment for U/t = 2.

cond-mat.str-el↗

arXiv2016

Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method

Ground state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum distribution are calculated for interaction strengths of U/t from 2 to 8, for a range of densities including half-filling and n = 0.3, 0.5, 0.6, 0.75, and 0.875. At half-filling, the results are numerically exact. Away from half-filling, the constrained path Monte Carlo method is employed to control the sign problem. Our results are obtained with several advances in the computational algorithm, which are described in detail. We discuss the advantages of generalized Hartree-Fock trial wave functions and its connection to pairing wave functions, as well as the interplay with different forms of Hubbard-Stratonovich decompositions. We study the use of different twist angle sets when applying the twist averaged boundary conditions. We propose the use of quasi-random sequences, which improves the convergence to the thermodynamic limit over pseudo-random and other sequences. With it and a careful finite size scaling analysis, we are able to obtain accurate values of ground state properties in the thermodynamic limit. Detailed results for finite-sized systems up to 16 \times 16 are also provided for benchmark purposes.

cond-mat.str-el↗

arXiv2016

Auxiliary-field quantum Monte Carlo calculations of the molybdenum dimer

Chemical accuracy is difficult to achieve for systems with transition metal atoms. Third row transition metal atoms are particularly challenging due to strong electron-electron correlation in localized d-orbitals. The Cr2 molecule is an outstanding example, which we previously treated with highly accurate auxiliary-field quantum Monte Carlo (AFQMC) calculations [Purwanto et al., J. Chem. Phys. 142, 064302 (2015)]. Somewhat surprisingly, computational description of the isoelectronic Mo2 dimer has also, to date, been scattered and less than satisfactory. We present high-level theoretical benchmarks of the Mo2 singlet ground state ($X ^1Σ_g^+$) and first triplet excited state ($a ^3Σ_u^+$), using the phaseless AFQMC calculations. Extrapolation to the complete basis set limit is performed. Excellent agreement with experimental spectroscopic constants is obtained. We also present a comparison of the correlation effects in Cr2 and Mo2.

physics.chem-ph↗

arXiv2016

Exact Numerical Results on the Ground State of Strongly Interacting Fermi Gases in Two Dimensions

Exact calculations are performed on the two-dimensional strongly interacting, unpolarized, uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. A new equation of state is obtained, with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs.~$k_F a$. The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary-fields in determinantal approaches is discussed.

cond-mat.quant-gas↗

arXiv2016

Rashba spin-orbit coupling, strong interactions, and the BCS-BEC crossover in the ground state of the two-dimensional Fermi Gas

The recent experimental realization of spin-orbit coupled Fermi gases provides a unique opportunity to study the interplay between strong interaction and SOC in a tunable, disorder-free system. We present here precision ab initio numerical results on the two-dimensional, unpolarized, uniform Fermi gas with attractive interactions and Rashba SOC. Using auxiliary-field quantum Monte Carlo and incorporating recent algorithmic advances, we carry out exact calculations on sufficiently large system sizes to provide accurate results systematically as a function of experimental parameters. We obtain the equation of state, the momentum distributions, the pseudo-spin correlations and the pairing wave functions. Our results help illuminate the rich pairing structure induced by SOC, and provide benchmarks for theory and guidance to future experimental efforts.

cond-mat.quant-gas↗

arXiv2015

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

cond-mat.str-el↗

arXiv2015

Infinite Variance in Fermion Quantum Monte Carlo Calculations

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, lattice QCD calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied upon to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple sub-areas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations turn out to have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a ``bridge link" to the imaginary-time path-integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

physics.comp-ph↗

arXiv2014

Quantum Monte Carlo calculations in solids with downfolded Hamiltonians

We present a systematic downfolding many-body approach for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using a frozen-core treatment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. We use the auxiliary-field quantum Monte Carlo (AFQMC) method to solve the downfolded Hamiltonian. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We further test the method by determining the spin gap in NiO, a challenging prototypical material with strong electron correlation effects. This approach greatly extends the reach of general, ab initio many-body calculations in materials.

cond-mat.mtrl-sci↗

arXiv2014

FFLO order in ultra-cold atoms in three-dimensional optical lattices

We investigate different ground-state phases of attractive spin-imbalanced populations of fermions in 3-dimensional optical lattices. Detailed numerical calculations are performed using Hartree-Fock-Bogoliubov theory to determine the ground-state properties systematically for different values of density, spin polarization and interaction strength. We first consider the high density and low polarization regime, in which the effect of the optical lattice is most evident. We then proceed to the low density and high polarization regime where the effects of the underlying lattice are less significant and the system begins to resemble a continuum Fermi gas. We explore the effects of density, polarization and interaction on the character of the phases in each regime and highlight the qualitative differences between the two regimes. In the high-density regime, the order is found to be of Larkin-Ovchinnikov type, linearly oriented with one characteristic wave vector but varying in its direction with the parameters. At lower densities the order parameter develops more structures involving multiple wave vectors.

cond-mat.quant-gas↗

arXiv2014

An Auxiliary-Field Quantum Monte Carlo Study of the Chromium Dimer

The chromium dimer (Cr2) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve, is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present a near-exact calculation of the potential energy curve (PEC) and ground state properties of Cr2, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set (CBS) limit is then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment.

physics.comp-ph↗

arXiv2014

CPMC-Lab: A Matlab Package for Constrained Path Monte Carlo Calculations

We describe CPMC-Lab, a Matlab program for the constrained-path and phaseless auxiliary-field Monte Carlo methods. These methods have allowed applications ranging from the study of strongly correlated models, such as the Hubbard model, to ab initio calculations in molecules and solids. The present package implements the full ground-state constrained-path Monte Carlo (CPMC) method in Matlab with a graphical interface, using the Hubbard model as an example. The package can perform calculations in finite supercells in any dimensions, under periodic or twist boundary conditions. Importance sampling and all other algorithmic details of a total energy calculation are included and illustrated. This open-source tool allows users to experiment with various model and run parameters and visualize the results. It provides a direct and interactive environment to learn the method and study the code with minimal overhead for setup. Furthermore, the package can be easily generalized for auxiliary-field quantum Monte Carlo (AFQMC) calculations in many other models for correlated electron systems, and can serve as a template for developing a production code for AFQMC total energy calculations in real materials. Several illustrative studies are carried out in one- and two-dimensional lattices on total energy, kinetic energy, potential energy, and charge- and spin-gaps.

cond-mat.str-el↗

arXiv2014

The Stability, Energetics, and Magnetic States of Cobalt Adatoms on Graphene

We investigate the stability and electronic properties of single Co atoms on graphene with near-exact many-body calculations. A frozen-orbital embedding scheme was combined with auxiliary-field quantum Monte Carlo to increase the reach in system sizes. Several energy minima are found as a function of the distance $h$ between Co and graphene. Energetics only permit the Co atom to occupy the top site at $h = 2.2$ Å in a high-spin $3d^{8}4s^{1}$ state, and the van der Waals region at $h = 3.3$ Å in a high-spin $3d^{7}4s^{2}$ state. The findings provide an explanation for recent experimental results with Co on free-standing graphene.

cond-mat.mtrl-sci↗

arXiv2014

Symmetry-projected Wave Functions in Quantum Monte Carlo Calculations

We consider symmetry-projected Hartree--Fock trial wave functions in constrained-path Monte Carlo (CPMC) calculations. Previous CPMC calculations have mostly employed Hartree--Fock (HF) trial wave functions, restricted or unrestricted. The symmetry-projected HF approach results in a hierarchy of wave functions with increasing quality: the more symmetries that are broken and restored in a self-consistent manner, the higher the quality of the trial wave function. This hierarchy is approximately maintained in CPMC calculations: the accuracy in the energy increases and the statistical variance decreases when further symmetries are broken and restored. Significant improvement is achieved in CPMC with the best symmetry-projected trial wave functions over those from simple HF. We analyze and quantify the behavior using the two-dimensional repulsive Hubbard model as an example. In the sign-problem-free region, where CPMC can be made exact but a constraint is deliberately imposed here, spin-projected wave functions remove the constraint bias. Away from half-filling, spatial symmetry restoration in addition to that of the spin lead to highly accurate results from CPMC. Since the computational cost of symmetry-projected HF trial wave functions in CPMC can be made to scale algebraically with system size, this provides a potentially general approach for accurate calculations in many-fermion systems.

cond-mat.str-el↗