arXiv subjects

Lucas K. Wagner

Publications and source records attributed to Lucas K. Wagner.

54 records · Page 3Linked to original sources

arXiv2016

Discovering correlated fermions using quantum Monte Carlo

It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.

cond-mat.str-el↗

arXiv2016

Using Local Operator Fluctuations to Identify Wave Function Improvements

A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying degrees of freedom that are not well-described by an initial trial state. We provide proof of concept implementations of this method by identifying the need for a Jastrow correlation factor, and implementing a selected multi-determinant wave function algorithm for small dimers that systematically decreases the variational energy. Selection of the two-particle excitations is done using quantum Monte Carlo within the presence of a Jastrow correlation factor, and without the need to explicitly construct the determinants. We also show how this technique can be used to design compact wave functions for transition metal systems. This method may provide a route to analyze and systematically improve descriptions of complex quantum systems in a scalable way.

cond-mat.str-el↗

arXiv2015

Towards a systematic assessment of errors in diffusion Monte Carlo calculations of semiconductors: case study of zinc selenide and zinc oxide

The fixed node diffusion Monte Carlo (DMC) method has attracted interest in recent years as a way to calculate properties of solid materials with high accuracy. However, the framework for the calculation of properties such as total energies, atomization energies, and excited state energies is not yet fully established. Several outstanding questions remain as to the effect of pseudopotentials, the magnitude of the fixed node error, and the size of supercell finite size effects. Here, we consider in detail the semiconductors ZnSe and ZnO and carry out systematic studies to assess the magnitude of the energy differences arising from controlled and uncontrolled approximations in DMC. The former include time step errors and supercell finite size effects for ground and optically excited states, and the latter include pseudopotentials, the pseudopotential localization approximation, and the fixed node approximation. We find that for these compounds, the errors can be controlled to good precision using modern computational resources, and that quantum Monte Carlo calculations using Dirac-Fock pseudopotentials can offer good estimates of both cohesive energy and the gap of these systems. We do however observe differences in calculated optical gaps that arise when different pseudopotentials are used.

cond-mat.mtrl-sci↗

arXiv2015

Phase Stability and Properties of Manganese Oxide Polymorphs: Assessment and Insights from Diffusion Monte Carlo

We present an analysis of the polymorphic energy ordering and properties of the rock salt and zincblende structures of manganese oxide using fixed node diffusion Monte Carlo (DMC). Manganese oxide is a correlated, antiferromagnetic material that has proven to be challenging to model from first principles across a variety of approaches. Unlike conventional density functional theory and some hybrid functionals, fixed node diffusion Monte Carlo finds the rock salt structure to be more stable than the zincblende structure, and thus recovers the correct energy ordering. Analysis of the site-resolved charge fluctuations of the wave functions according to DMC and other electronic structure descriptions give insights into elements that are missing in other theories. While the calculated band gaps within DMC are in agreement with predictions that the zincblende polymorph has a lower band gap, the gaps themselves overestimate reported experimental values.

cond-mat.mtrl-sci↗

arXiv2015

Ground state of doped cuprates from first principles quantum Monte Carlo calculations

The author reports on new high-fidelity simulations of charge carriers in the high-T$_c$ cuprate materials using quantum Monte Carlo techniques applied to the first principles Hamiltonian. With this high accuracy technique, the doped ground state is found to be a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface and charge inhomogeneity in these materials. The spin polaron has some unique features that should be visible in X-ray, EELS, and neutron experiments. The results contained in this paper comprise an accurate first principles derived paradigm from which to study superconductivity in the cuprates.

cond-mat.str-el↗

arXiv2015

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio Quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding (AIDMD). For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard $U^{*}/t$ to be $1.3 \pm 0.2$, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large scale calculations using techniques designed for lattice models.

cond-mat.str-el↗

arXiv2015

Computation of the correlated metal-insulator transition in vanadium dioxide from first principles

Vanadium dioxide(VO$_2$) is a paradigmatic example of a strongly correlated system that undergoes a metal-insulator transition at a structural phase transition. To date, this transition has necessitated significant post-hoc adjustments to theory in order to be described properly. Here we report standard state-of-the-art first principles quantum Monte Carlo (QMC) calculations of the structural dependence of the properties of VO$_2$. Using this technique, we simulate the interactions between electrons explicitly, which allows for the metal-insulator transition to naturally emerge, importantly without ad-hoc adjustments. The QMC calculations show that the structural transition directly causes the metal-insulator transition and a change in the coupling of vanadium spins. This change in the spin coupling results in a prediction of a momentum-independent magnetic excitation in the insulating state. While two-body correlations are important to set the stage for this transition, they do not change significantly when VO$_2$ becomes an insulator. These results show that it is now possible to account for electron correlations in a quantitatively accurate way that is also specific to materials.

cond-mat.str-el↗

arXiv2014

The effect of electron correlation on the electronic structure and spin-lattice coupling of the high-T$_c$ cuprates: quantum Monte Carlo calculations

Electron correlation effects are particularly strong in the high temperature superconducting materials. Devising an accurate description of these materials has long been a challenge, with these strong correlation effects historically being considered impossible or impractical to simulate computationally. Using quantum Monte Carlo techniques, we have explicitly simulated electron correlations in several cuprate materials from first principles. These simulations accurately reproduce many important physical quantities about these materials, including the interaction-induced gap and the superexchange coupling between copper spins, with no additional parameters beyond fundamental constants. We further investigate the dimensionless spin-lattice coupling parameter in the parent materials, showing that it varies dramatically between 0.1 and 1.0 depending on the interlayer. This result indicates that the lattice and magnetic degrees of freedom are not independent in these systems, which may have ramifications for the origin of superconductivity.

cond-mat.str-el↗

arXiv2012

Types of single particle symmetry breaking in transition metal oxides due to electron correlation

Very accurate wave functions are calculated for small transition metal oxide molecules. These wave functions are decomposed using reduced density matrices to study the underlying correlation of electrons. The correlation is primarily of left-right type between the transition metals and the oxygen atoms, which is mediated by excitations from the nominal single Slater ground state into antibonding and d-type orbitals. In a localized representation, this correlation manifests itself in a 2-electron hopping term that is off-diagonal. This term is of similar magnitude to the commonly considered Hubbard-type on-site interaction.

cond-mat.str-el↗

arXiv2012

Point-Defect Optical Transitions and Thermal Ionization Energies from Quantum Monte Carlo Methods: Application to F-center Defect in MgO

We present an approach to calculation of point defect optical and thermal ionization energies based on the highly accurate quantum Monte Carlo methods. The use of an inherently many-body theory that directly treats electron correlation offers many improvements over the typically-employed density functional theory Kohn-Sham description. In particular, the use of quantum Monte Carlo methods can help overcome the band gap problem and obviate the need for ad-hoc corrections. We demonstrate our approach to the calculation of the optical and thermal ionization energies of the F-center defect in magnesium oxide, and obtain excellent agreement with experimental and/or other high-accuracy computational results.

cond-mat.mtrl-sci↗

arXiv2010

Quantum Monte Carlo for minimum energy structures

We present an efficient method to find minimum energy structures using energy estimates from accurate quantum Monte Carlo calculations. This method involves a stochastic process formed from the stochastic energy estimates from Monte Carlo that can be averaged to find precise structural minima while using inexpensive calculations with moderate statistical uncertainty. We demonstrate the applicability of the algorithm by minimizing the energy of the H2O-OH- complex and showing that the structural minima from quantum Monte Carlo calculations affect the qualitative behavior of the potential energy surface substantially.

physics.comp-ph↗

arXiv2009

Theoretical study of electronic and atomic structures of (MnO)n

We calculate the electronic and atomic structure of (MnO)n (n=1-4) using the HF exchange, VWN, PBE and B3LYP exchange-correlation functionals. We also perform diffusion Monte Carlo calculation to evaluate more accurate energies. We ompare these results and discuss the accuracy of the exchange-correlation functionals.

cond-mat.mtrl-sci↗

arXiv2008

A microscopic description of light induced defects in amorphous silicon solar cells

Using a combination of quantum and classical computational approaches, we model the electronic structure in amorphous silicon in order gain understanding of the microscopic atomic configurations responsible for light induced degradation of solar cells. We demonstrate that regions of strained silicon bonds could be as important as dangling bonds for creating traps for charge carriers. Further, our results show that defects are preferentially formed when a region in the amorphous silicon contains a hole and a light-induced excitation. These results agree with the puzzling dependencies on temperature, time, and pressure observed experimentally.

cond-mat.mtrl-sci↗

arXiv2007

QWalk: A Quantum Monte Carlo Program for Electronic Structure

We describe QWalk, a new computational package capable of performing Quantum Monte Carlo electronic structure calculations for molecules and solids with many electrons. We describe the structure of the program and its implementation of Quantum Monte Carlo methods. It is open-source, licensed under the GPL, and available at the web site http://www.qwalk.org

physics.comp-ph↗

arXiv2007

Transition metal oxides using quantum Monte Carlo

The transition metal-oxygen bond appears prominently throughout chemistry and solid-state physics. Many materials, from biomolecules to ferroelectrics to the components of supernova remnants contain this bond in some form. Many of these materials' properties strongly depend on fine details of the TM-O bond and intricate correlation effects, which make accurate calculations of their properties very challenging. We present quantum Monte Carlo, an explicitly correlated class of methods, to improve the accuracy of electronic structure calculations over more traditional methods like density functional theory. We find that unlike s-p type bonding, the amount of hybridization of the d-p bond in TM-O materials is strongly dependant on electronic correlation.

cond-mat.str-el↗

arXiv2006

Energetics and Dipole Moment of Transition Metal Monoxides by Quantum Monte Carlo

The transition metal-oxygen bond appears very prominently throughout chemistry and solid-state physics. Many materials, from biomolecules to ferroelectrics to the components of supernova remnants contain this bond in some form. Many of these materials' properties depend strongly on fine details of the TM-O bond, which makes accurate calculations of their properties very challenging. Here we report on highly accurate first principles calculations of the properties of TM monoxide molecules within fixed-node Diffusion Monte Carlo and Reptation Monte Carlo.

cond-mat.mtrl-sci↗

arXiv2005

Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies

A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes for some cases of two electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^4S(p^3)$ state using appropriate coordinate maps and wavefunction symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into 3D space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wavefunctions.

cond-mat.other↗

arXiv2004

Quantum Monte Carlo study of MnO solid

Electronic structure of the manganese oxide solid is studied by the quantum Monte Carlo (QMC) methods. The trial wavefunctions are built using orbitals from unrestricted Hartree-Fock and Density Functional Theory, and the electron-electron correlation is recovered by the fixed-node QMC. The correlation effects are significant and QMC estimations of the gap and cohesion show a very good agreement with experiment. Comparison with hybrid functional results points out the importance of the exact exchange for improvement of the Density Functional description of transition metal oxide systems.

cond-mat.str-el↗