Session P20: Quantum Many-Body Systems and Methods III

QMC calculations of the dynamical local field factor of the 2D electron gas

We develop a new quantum Monte Carlo method to calculate imaginary time correlation functions for fermions in continuous space in order to access spectral functions. Linear response in imaginary time is obtained based on the variational expression of the thermal density matrix. The exact dynamics is recovered in the non-interacting limit. We apply our new method to the electron gas in two dimensions in the high and low density region and calculate the density fluctuations including many-body correlations in the density matrix. The dynamic structure factor can be accessed by analytic continuation. Our results provides accurate estimation of the dynamical local field factor which quantifies corrections to the RPA approximation.   

Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperatures

Recent advances in warm dense matter physics, e.g. laser compressed matter, lead to an increasing interest in the description of correlated, degenerate electrons at finite temperatures. The uniform electron gas (UEG) is of key relevance for the understanding of such systems. Accurate thermodynamic data for the UEG are essential for the development of the finite-temperature density functional theory (FT-DFT). \\{} Based on first principles, the Configuration PIMC approach (CPIMC) allows for the exact computation of thermodynamic properties of strongly degenerate fermionic many-body systems in the highly degenerate regime [1]. We present CPIMC exchange-correlation energies for the UEG [2] and compare our results with previous restricted path integral Monte Carlo (RPIMC) [3] and recently published permutation-blocking PIMC (PB-PIMC) [4] data. We show that the complementary sign problem of the CPIMC and PB-PIMC methods allows for results with an unprecedented accuracy in a wide range of temperatures and densities. \\{} [1] Contrib. Plasma Phys. \textbf{51}, 687 (2011).\\{} [2] Phys. Rev. Lett. \textbf{115}, 130402 (2015). \\{} [3] Phys. Rev. Lett. \textbf{110}, 146405 (2013). \\{} [4] arXiv:1508.03221 (2015).   

Identification of polaronic defects in wide band gap semiconductors via diffusion Monte Carlo

Polaronic defects are important to understanding a wide variety of properties in semiconductors; for instance they are closely coupled to electron phonon interactions and can greatly affect carrier concentrations and mobilities. The formation of a polaronic defect in a semiconductor is an interesting phenomenon because it incorporates a trade off between electron localization and structural relaxation. Because of its small energy scale and the localized nature of polaronic defect levels, accurately describing polaronic defects in semiconductors requires high accuracy first principle calculation methods. We demonstrate the use of the fixed node diffusion Monte Carlo (DMC) method to the identification of polaronic nitrogen defects in the wide band gap semiconductor zinc oxide. Using DMC, we can demonstrate that nitrogen defects in ZnO are subject to a symmetry-breaking Jahn-Teller distortion, which deepens the defect level in the band gap. Our DMC results for defect transition levels and optical transitions are in good agreement with recent experiments. Our results demonstrates that highly accurate treatment of electron correlation can improve predicition of defect properties in challenging semiconductor materials.   

Diffusion Monte Carlo study of the metal-insulator transition in stretched graphene

At low energies and equilibrium geometries, graphene is well-described by a single-band Hubbard model[1], with U/t~1.4, which is well within the semimetal regime. One would expect that under tensile stress, U/t should increase and a transition from semimetal to Mott insulator should occur. However, the bonding $\sigma$ electrons are also affected by the stretching and may affect the applicability of the single-band model. At the same time, the critical region near the metal-insulator transition is a highly multi-determinantal ground state which is a challenging case for fixed node diffusion Monte Carlo simulations. We address progress on both these points by assessing a number of wave functions for the critical region around the transition and assessing the validity of the single-band Hubbard model using the method of Ref 1. [1]. Changlani, Zheng, and Wagner, J. Chem. Phys. 143, 102814 (2015).   

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

Strongly correlated electron systems driven out of equilibrium have attracted much attention because of potential routes to realizing intriguing phenomena that are not attainable in the equilibrium. To treat such systems, we propose a time-dependent trial wave function with many variational parameters for the time-dependent variational Monte Carlo (t-VMC) method [1]. As the trial state, we adopt the generalized pair-product wave function with correlation factors and quantum-number projections. This trial wave function has been proven to accurately describe ground states of strongly correlated electron systems [2]. To show the accuracy and efficiency of our trial wave function in nonequilibrium states as well, we present our benchmarks for relaxation dynamics during and after interaction quench protocols of the Hubbard models both at and away from half-filling. We find that our trial wave function well reproduces the exact results for the time evolution of physical quantities such as momentum distribution and superconducting correlations. We discuss how the accuracy depends on the level of trial wave functions. [1] K. Ido, T. Ohgoe, and M. Imada, arXiv: 1507.00274. [2] D. Tahara and M. Imada, J. Phys. Soc. Jpn. 77,114701(2008).   

Stochastic Approximation of Dynamical Exponent at Quantum Critical Point

We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent $z$. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional $S=1/2$ quantum $XY$ model, or equivalently the hard-core boson system, in uniform and staggered magnetic fields is investigated in the combination of the world-line quantum Monte Carlo worm algorithm. In the absence of a uniform magnetic field, we obtain the fully consistent result with the Lorentz invariance at the quantum critical point, $z=1$. Under a finite uniform magnetic field, on the other hand, the dynamical exponent becomes two, and the mean-field universality with effective dimension (2+2) governs the quantum phase transition. We will discuss also the system with random magnetic fields, or the dirty boson system, bearing a non-trivial dynamical exponent.\\ Reference: S. Yasuda, H. Suwa, and S. Todo {\it Phys. Rev. B} {\bf 92}, 104411 (2015); arXiv:1506.04837   

Auxiliary-field based trial wave functions in quantum Monte Carlo simulations

We propose a simple scheme for generating correlated multi-determinant trial wave functions for quantum Monte Carlo algorithms. The method is based on the Hubbard-Stratonovich transformation which decouples a two-body Jastrow-type correlator into one-body projectors coupled to auxiliary fields. We apply the technique to generate stochastic representations of the Gutzwiller wave function, and present benchmark resuts for the ground state energy of the Hubbard model in one dimension. Extensions of the proposed scheme to chemical systems will also be discussed.   

Diffusion Quantum Monte Carlo predictions for bulk MnNiO$_{\mathrm{3}}$

MnNiO$_{\mathrm{3}}$ is a strongly correlated transition metal oxide that has recently been investigated theoretically for its potential application as an oxygen-evolution photo-catalyst. However, there is no experimental report on critical quantities like its band gap or its bulk modulus. Recent theoretical predictions with standard functionals, such as PBE$+$U and HSE show large discrepancies in the band-gaps (about 1.23 eV), depending on the nature of the functional used. Hence, there is clearly a need for an accurate quantitative prediction of the band-gap in order to decide its usefulness as a photo-catalyst. In this work, we present Diffusion Quantum Monte Carlo (DMC) study of the bulk properties of MnNiO$_{\mathrm{3}}$. This includes the quasiparticle band gap for the two spin channels, the equilibrium lattice parameter and the bulk modulus. The DMC approach has already been shown to achieve excellent agreement with experimental results for other oxides such as ZnO NiO and Fe$_{\mathrm{2}}$O$_{\mathrm{3}}$. To our knowledge, MnNiO$_{\mathrm{3}}$ is the first case where this theory is applied before experiments are done.   

Fragmented Molecular Orbital with Diffusion Monte Carlo for large molecular systems

Performing accurate quantum mechanics (QM) calculations on larger and larger systems, while maintaining a high level of accuracy is an ongoing effort in many ab initio fields. Many different attempts have been made to develop highly scalable and accurate methods. The fragment molecular orbital (FMO) method is an ab initio method capable of taking advantage of modern supercomputers, such as the Blue Gene Q system Mira at the Argonne National Laboratory Leadership Computing Facility (ALCF). FMO is based on dividing molecules into fragments and performing ab initio calculations on fragments, their dimers and, optionally, trimers. This decomposition makes it possible to perform QM calculations of real size biological molecules. In contrast to many other fragment-based methods, the effect of the environment is rigorously accounted for by computing the electrostatic potential (ESP) due to remaining fragments that are not explicitly included in a given monomer, dimer, or trimer calculation. The use of highly accurate levels of theory, such as Diffusion Monte Carlo (DMC-QMC), in conjunction with FMO allows for the goal of highly scalable and accurate all electron calculations demonstrated in this study, on a variety of relevant systems (H2O)[3-6] and protein using GAMESS and QMCPACK.   

Improved measurement scheme of the self energy in the worm-sampled hybridization-expansion quantum Monte Carlo

Hybridization-expansion continuous-time quantum Monte Carlo (CT-HYB) is a popular approach in real material researches because it allows to deal with non-density-density-type interaction. In the conventional CT-HYB, we measure Green's function and find the self energy from the Dyson equation. Because one needs to compute the inverse of the statistical data in this approach, obtained self energy is very sensitive to statistical noise. For that reason, the measurement is not reliable except for low frequencies. Such an error can be suppressed by measuring a special type of higher-order correlation function and is implemented for density-density-type interaction [1]. With the help of the recently reported worm-sampling measurement [2], we developed an improved self energy measurement scheme which can be applied to any type of interactions. As an illustration, we calculated the self energy for the 3-orbital Hubbard-Kanamori-type Hamiltonian with our newly developed method. This work was supported by NRF of Korea (Grant No. 2011-0018306) and KISTI supercomputing center (Project No. KSC-2015-C3-039). [1] H. Hafermann et al., Phys. Rev. B, 85, 205106 (2012) [2] P. Gunacker et al., Phys. Rev. B, 92, 155102 (2015)   

Reducing memory demands of splined orbitals in diffusion Monte Carlo calculations

Quantum Monte Carlo calculations of defect properties of transition metal oxides have become feasible in recent years due to increases in computing power. As the system size has grown, availability of on-node memory has become a limiting factor. The main growth in memory demand stems from the B-spline representation of the single particle orbitals, especially for heavier elements such as transition metals where semi-core states are present. Despite the associated memory costs, splines are computationally efficient. In this work, we explore alternatives to reduce the memory usage of splined orbitals without significantly affecting numerical fidelity or computational efficiency. For the example case of bulk MnO we have currently achieved a memory savings of 50\% while only increasing the overall computational cost of the simulation by 15\%.   

Quantum Monte Carlo Computations of the (Mg$_{1-X}$Fe$_{X})$SiO$_{3}$ Perovskite to Post-perovskite Phase Boundary

We have computed total energies of FeSiO$_{3}$ and MgSiO$_{3}^{[1]}$ perovskite and post-perovskite using diffusion Monte Carlo with the qmcpack GPU code. In conjunction with DFT$+$U computations for intermediate compositions (Mg$_{1-X}$Fe$_{X})$SiO$_{3}$ and phonons computed using density functional perturbation theory (DFPT) with the pwscf code, we have derived the chemical potentials of perovskite (Pv) and post-perovskite (PPv) (Mg$_{1-X}$Fe$_{X})$SiO$_{3}$ and computed the binary phase diagram versus P, T, and X using a non-ideal solid solution model. The finite temperature effects were considered within quasi-harmonic approximation (QHA). Our results show that ferrous iron stabilizes PPv and lowers the Pv-PPv transition pressure, which is consistent with previous theoretical and some experimental studies. We will discuss the correlation between the Earth's D” layer and the Pv to PPv phase boundary. Computations were performed on XSEDE machines, and on the Oak Ridge Leadership Computing Facility (OLCF) machine Titan under project CPH103geo of INCITE program. [1] Lin \textit{et al.}. Phys. Rev. B 90(18), 184103 (2014)   

Fixed-phase vs fixed-node quantum Monte Carlo with local and nonlocal interactions

We study several systems that can be formulated in the fixed-phase and/or fixed-node framework in quantum Monte Carlo calculations. In particular, we try to understand the differences between the biases caused by these approximations that result from using complex vs real trial wave functions. One system is a model that enables us to construct systematically the same type of nodal errors in both real and complex formalism. The errors are comparably similar whenever trial functions are correspondingly accurate. Another aspect of the fixed-phase vs fixed-node approximations is studied for systems with nonlocal operators such as with pseudopotentials and/or spin-orbit effects. We specify how to obtain variational formulation for complex wave functions and nonlocal operators in a manner analogous to the fixed-node calculations with T-moves algorithm. In particular, we show that the fixed-phase/fixed-node is the primary condition for proving that the upper bound property holds.