Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session Y34: Precision Many Body Physics VIFocus
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Sponsoring Units: DCOMP DAMOP DCMP Chair: Sergei Iskakov, Univ of Michigan - Ann Arbor Room: LACC 409A |
Friday, March 9, 2018 11:15AM - 11:51AM |
Y34.00001: Self-energy embedding theory (SEET) Invited Speaker: Dominika Zgid I will present a discussion of self-energy embedding theory (SEET) which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower cost. We have applied SEET to both molecular and periodic examples where commonly our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Such a self-energy separation is very general and to make this procedure applicable to multiple systems a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach high accuracy. |
Friday, March 9, 2018 11:51AM - 12:03PM |
Y34.00002: Effect of nodal surface on the geometry of antiferromagnetic iron oxide Joshua Townsend, Luke Shulenburger, Thomas Mattsson, Ken Esler, Ronald Cohen We report quantum variational and diffusion Monte Carlo calculations of antiferromagnetic iron oxide (FeO) which offer a test of the accuracy and predictive power of a single slater-jastrow determinant representation of a highly correlated many-body wave function. |
Friday, March 9, 2018 12:03PM - 12:15PM |
Y34.00003: Quantum Monte Carlo Beyond Fixed-Node/Phase Approximations Using Extended Configuration Spaces and Residuals Lubos Mitas, Cody Melton, Michael Bennett Electronic structure quantum Monte Carlo (QMC) that is based on sampling particle configurations has a number of desired properties such as direct access to interparticle correlations and pointwise information about deviations of the local energy from an estimated eigenvalue. The price for these advantages is the fixed-node/phase approximation that is typically used to eliminate the well-known fermion sign/complex value problems. We explore possibilities of recently introduced spinor-based QMC formulation to find improvements over the fixed-node/phase results. One direction is a spinor-based released-node method that enables one to correct part of the fixed-node error by tuning the fixed-phase sampling of configurations in overcomplete continuous spin representation. Another strategy is based on the use of residuals froma variational treatment to improve the trial function as well as to increase efficiency of the estimators. An analysis of results from these calculations enables us to identify the types of fixed-node biases commonly present in trial functions and to estimate corresponding improvements in accuracy and efficiency. |
Friday, March 9, 2018 12:15PM - 12:27PM |
Y34.00004: Multideterminant diffusion Monte Carlo applied to Molecules and Solids Anouar Benali, Thomas Applencourt, Jeongnim Kim, Anthony Scemama, Michel Caffarel In the past decade, fixed-node Diffusion Monte Carlo using a single Slater-Jastrow determinant as a trial wavefunction has proven to reproduce systematically (within 50meV) the energies of a wide range of molecules and solids. While it has been demonstrated for molecular systems that the path to chemical accuracy (<1Kcal/mol) relys on improving the accuracy of the nodal surface, which can be achieved using a multideterminants trial wavefunction from MCSCF or Selected CI, no such calculations have been attempted on a solid. In this talk, we will discuss the effect of using a multi-determinant selected CI trial wavefunctions, generated with Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI),in diffusion Monte Carlo (DMC) on the energies of molecules and solids. This first study will allow us to analyze the feasibility, advantages and size consistency issues when using large multideterminants expansion in QMC at the era of exascale computers. |
Friday, March 9, 2018 12:27PM - 12:39PM |
Y34.00005: Improving the Accuracy of AFQMC with Non-Orthogonal Multi-Determinant Wave Functions Edgar Landinez Borda, Matthew Otten, Cyrus Umrigar, Miguel Morales We explore the use of trial wave functions in Auxiliary-Field Quantum Monte Carlo constructed from non-orthogonal Slater determinant expansions. The use of these wave functions leads to systematically increased accuracy with a reduced number of terms and a compact representation, when compared to traditional determinant expansions constructed from particle-hole excitations. We demonstrate significantly improved accuracy when compared to traditional trial wave-functions, as well as systematically improvable results in both strongly correlated molecular calculations and periodic systems. First, we compute the isomerization path of the [Cu_{2}O_{2}]^{+2} molecule and compare the profile of relative energies along the path against DMRG, CR-CC and SPHF calculations. This problem is well known because the accurate calculation of the correlation energy along the path is challenging. The present methodology exhibits versatility and good agreement using only several tens to hundreds of determinants. We also test the methodology in a periodic system performing calculations for Silicon in the diamond phase. We compare against Coupled Cluster and converged selected CI calculations. As shown, the method is capable of reaching sub-mHa accuracy even when a modest number of determinant is used. |
Friday, March 9, 2018 12:39PM - 12:51PM |
Y34.00006: Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo Yuan Liu, Brenda Rubenstein Predicting finite temperature (FT) properties of molecules and solids is critical to understanding many physical and chemical processes. However, developing accurate, yet efficient theoretical approaches for FT applications remains an outstanding challenge. Aside from FT mean field theories that have limited accuracy and FT Full Configuration Interaction with exponential scaling, proper ways to generalize various post Hartree-Fock theories to FT is still an open problem. Furthermore, FT generalizations of Density Functional Theory, considered to be promising candidates for future large scale simulation, require additional benchmarking against more accurate methods. |
Friday, March 9, 2018 12:51PM - 1:03PM |
Y34.00007: Accelerating the use of multi-determinant trial wave functions in auxiliary-field quantum Monte Carlo calculations Hao Shi, Shiwei Zhang The trial wave function is used in auxiliary-field quantum Monte Carlo (AFQMC) method to initialize the projection, control the sign/phase problem, and serve as the starting point for back-propagation. Typically a single determinant wave function is used. The computation and memory costs of using multi-determinant trial wave functions tends to grow linearly with the number of Slater determinants. An efficient algorithm is proposed for AFQMC simulations with configuration interaction trial wave functions. Large numbers of Slater determinants can be reached with much smaller memory usage and computation time. Systematic tests can be made by increasing the number of determinants in the trial wave function. Thousands to millions of determinants can be reached in molecular systems. The error from the approximation to control the sign/phase problem often becomes negligible with the new capability, and the Monte Carlo fluctuation can be much reduced. We illustrate this with examples on atoms and molecules, including challenging transition metal systems. |
Friday, March 9, 2018 1:03PM - 1:15PM |
Y34.00008: Non-Orthogonal Determinant Multi-Slater-Jastrow Wave Functions in QMC Shivesh Pathak, Lucas Wagner The efficiency of ab-initio quantum Monte Carlo (QMC) algorithms benefits greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of using non-orthogonal determinants to create more compact wave functions than standard multi-Slater-Jastrow trial wave functions. As a test case, we compute variational and diffusion Monte Carlo (DMC) energies of a C2 molecule. For a given multi-determinant expansion, we find that allowing the determinants to be non-orthogonal results in a fairly consistent ~ 0.4 eV improvement in the variational energy and ~ 0.2 eV improvement in the DMC energy. Our calculations indicate that trial wave functions with non-orthogonal determinants may noticeably improve computed energies in a QMC calculation when compared to their traditional orthogonal counterparts. |
Friday, March 9, 2018 1:15PM - 1:27PM |
Y34.00009: Automated Construction of U(1)-invariant Matrix-Product Operators from Graph Representations Sebastian Paeckel, Thomas Koehler, Salvatore Manmana We present an algorithmic construction scheme for matrix-product-operator (MPO) representations of arbitrary U(1)-invariant operators in case a finite-states-machine (FSM) formulation exists. The method automatizes two major construction steps: |
Friday, March 9, 2018 1:27PM - 1:39PM |
Y34.00010: Magnetism and metal-insulator transition in nickel oxide from Auxiliary-Field Quantum Monte Carlo (AFQMC) studies Shuai Zhang, Fionn Malone, Miguel Morales NiO is of great interests in condensed matter physics. Within single particle mean-field framework, one can obtain its insulating anti-ferromagnetic ground state and correct band gap, magnetic momentum, or lattice constant by adjusting exchange correlation interactions. However, it is challenging to re-produce all the properties using the same setup, and the predicted magnetic and metallic transitions are questionable. It demands physically accurate and computationally efficient many-body algorithms to tackle these questions. AFQMC works in second quantized representation and has been shown promising in solving extended systems with high accuracy [comparable to those of CCSD(T) and FCI] and low scaling (N3-N4). As an integral part of the Center for Predictive Simulation of Functional Materials (CPSFM), we develop efficient algorithms based on AFQMC and massively parallel supercomputer platforms and study transition metal oxides. We control the phase and sign problem with the phaseless formalism. As an example, we calculate the energy and magnetism of NiO in different magnetic states and upon volume changes. Our results agree well with experiments and can benchmark future theoretical investigations. |
Friday, March 9, 2018 1:39PM - 1:51PM |
Y34.00011: Eight-valence electron configuration-interaction many-body perturbation theory calculations of noble-gas atoms Igor Savukov Excited states of noble-gas atoms present certain difficulties to configuration-interaction many-body perturbation theory (CI-MBPT). One specific problem is that in formalism of particle-hole CI-MBPT, the perturbation theory for hole states does not converge well. One solution was proposed to use either all-order methods [1] or to modify MBPT denominators [2]. In the current work, on example of Ar, we find that this problem can be solved by treating 3s and 3p electrons as valence electrons (8 total), and by including the residual interactions with 1s, 2s, 2p core electrons via MBPT. The configuration space grows very quickly with the number of allowable excitations, so we impose certain constrains on them, for example by excluding triplet excitations, to have manageable CI space. We find that with our approach we can obtain energies, g factors, and matrix elements in reasonable agreement with experiments and other calculations. |
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