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Lubos Mitas

Publications and source records attributed to Lubos Mitas.

At least 55 records · Page 3Linked to original sources
arXiv2013

Fixed-node errors in quantum Monte Carlo: interplay of electron density and node nonlinearities

We elucidate the origin of large differences (two-fold or more) in the fixed-node errors between the first- vs second-row systems for single-configuration trial wave functions in quantum Monte Carlo calculations. This significant difference in the fixed-node biases is studied across a set of atoms, molecules, and also Si, C solid crystals. The analysis is done over valence isoelectronic systems that share similar correlation energies, bond patterns, geometries, ground states, and symmetries. We show that the key features which affect the fixed-node errors are the differences in electron density and the degree of node nonlinearity. The findings reveal how the accuracy of the quantum Monte Carlo varies across a variety of systems, provide new perspectives on the origins of the fixed-node biases in electronic structure calculations of molecular and condensed systems, and carry implications for pseudopotential constructions for heavy elements

physics.comp-ph↗
arXiv2011

Variational Monte Carlo for spin-orbit interacting systems

Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a general variational Monte Carlo approach is here introduced that treats in an efficient and very accurate way the spin degrees of freedom in atoms when spin orbit effects are included in the Hamiltonian describing the electronic structure. We illustrate the algorithm on the evaluation of the spin-orbit splittings of isolated carbon and lead atoms. In the case of the carbon atom, we investigate the differences between the inclusion of spin-orbit in its realistic and effective spherically symmetrized forms. The method exhibits a very good accuracy in describing the small energy splittings, opening the way for a systematic quantum Monte Carlo studies of spin-orbit effects in atomic systems.

cond-mat.str-el↗
arXiv2011

Impact of the Electron Density on the Fixed-Node Errors in Quantum Monte Carlo

We analyze the effect of increasing charge density on the Fixed Node Errors in Diffusion Monte Carlo by comparing FN-DMC calculations of the total ground state energy on a 4 electron system done with a Hartree-Fock based trial wave function to calculations by the same method on the same system using a Configuration Interaction based trial wave function. We do this for several different values of nuclear charge, Z. The Fixed Node Error of a Hartree-Fock trial wave function for a 4 electron system increases linearly with increasing nuclear charge.

physics.chem-ph↗
arXiv2011

Precision benchmark calculations for four particles at unitarity

The unitarity limit describes interacting particles where the range of the interaction is zero and the scattering length is infinite. We present precision benchmark calculations for two-component fermions at unitarity using three different ab initio methods: Hamiltonian lattice formalism using iterated eigenvector methods, Euclidean lattice formalism with auxiliary-field projection Monte Carlo, and continuum diffusion Monte Carlo with fixed and released nodes. We have calculated the ground state energy of the unpolarized four-particle system in a periodic cube as a dimensionless fraction of the ground state energy for the non-interacting system. We obtain values 0.211(2) and 0.210(2) using two different Hamiltonian lattice representations, 0.206(9) using Euclidean lattice, and an upper bound of 0.212(2) from fixed-node diffusion Monte Carlo. Released-node calculations starting from the fixed-node result yield a decrease of less than 0.002 over a propagation of 0.4/E_F in Euclidean time, where E_F is the Fermi energy. We find good agreement among all three ab initio methods.

cond-mat.quant-gas↗
arXiv2011

Atomic Fermi gas at the unitary limit by quantum Monte Carlo methods: Effects of the interaction range

We calculate the ground-state properties of unpolarized two-component Fermi gas by the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find $E/E_{\rm free}$ to be 0.212(2), 0.407(2), 0.409(3) and 0.398(3) for 4, 14, 38 and 66 atoms, respectively. Our results indicate that the dependence of the total energy on the effective range is sizable and the extrapolation is therefore quite important. In order to test the quality of nodal surfaces and to estimate the impact of the fixed-node approximation we perform released-node DMC calculations for 4 and 14 atoms. Analysis of the released-node and the fixed-node results suggests that the main sources of the fixed-node errors are long-range correlations which are difficult to sample in the released-node approaches due to the fast growth of the bosonic noise. Besides energies, we evaluate the two-body density matrix and the condensate fraction. We find that the condensate fraction for the 66 atom system converges to 0.56(1) after the extrapolation to the zero interaction range.

cond-mat.quant-gas↗
arXiv2010

Applications of quantum Monte Carlo methods in condensed systems

The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of the present-day high-performance computing systems. This review article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to electronic structure of solids and other extended many-particle systems.

physics.comp-ph↗
arXiv2010

Electronic structure quantum Monte Carlo

Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion Hamiltonians. Some of the key QMC achievements include direct treatment of electron correlation, accuracy in predicting energy differences and favorable scaling in the system size. Calculations of atoms, molecules, clusters and solids have demonstrated QMC applicability to real systems with hundreds of electrons while providing 90-95% of the correlation energy and energy differences typically within a few percent of experiments. Advances in accuracy beyond these limits are hampered by the so-called fixed-node approximation which is used to circumvent the notorious fermion sign problem. Many-body nodes of fermion states and their properties have therefore become one of the important topics for further progress in predictive power and efficiency of QMC calculations. Some of our recent results on the wave function nodes and related nodal domain topologies will be briefly reviewed. This includes analysis of few-electron systems and descriptions of exact and approximate nodes using transformations and projections of the highly-dimensional nodal hypersurfaces into the 3D space. Studies of fermion nodes offer new insights into topological properties of eigenstates such as explicit demonstrations that generic fermionic ground states exhibit the minimal number of two nodal domains. Recently proposed trial wave functions based on Pfaffians with pairing orbitals are presented and their nodal properties are tested in calculations of first row atoms and molecules. Finally, backflow "dressed" coordinates are introduced as another possibility for capturing correlation effects and for decreasing the fixed-node bias.

cond-mat.other↗
arXiv2010

Wave functions for quantum Monte Carlo calculations in solids: Orbitals from density functional theory with hybrid exchange-correlation functionals

We investigate how the fixed-node diffusion Monte Carlo energy of solids depends on single-particle orbitals used in Slater--Jastrow wave functions. We demonstrate that the dependence can be significant, in particular in the case of 3d transition-metal compounds, which we adopt as examples. We illustrate how exchange-correlation functionals with variable exact-exchange component can be exploited to reduce the fixed-node errors. On the basis of these results we argue that the fixed-node quantum Monte Carlo provides a variational approach for optimization of effective hamiltonians with parameters.

cond-mat.mtrl-sci↗
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↗
arXiv2007

Quantum Monte Carlo calculations of structural properties of FeO under pressure

We determine the equation of state of stoichiometric FeO employing the diffusion Monte Carlo method. The fermionic nodes are fixed to those of a wave function having the form of a single Slater determinant. The calculated ambient pressure properties (lattice constant, bulk modulus and cohesive energy) agree very well with available experimental data. At approximately 65 GPa, the lattice structure is found to change from rocksalt type (B1) to NiAs based (inverse B8).

cond-mat.mtrl-sci↗
arXiv2007

Persistent current of correlated electrons in mesoscopic ring with impurity

The persistent current of correlated electrons in a continuous one-dimensional ring with a single scatterer is calculated by solving the many-body Schrodinger equation for several tens of electrons interacting via the electron-electron (e-e) interaction of finite range. The problem is solved by the configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. The CI and DMC results are in good agreement. In both cases, the persistent current $I$ as a function of the ring length $L$ exhibits the asymptotic dependence $I \propto L^{-1-α}$ typical of the Luttinger liquid, where the power $α$ depends only on the e-e interaction. The numerical values of $α$ agree with the known formula of the renormalisation-group theory.

cond-mat.mes-hall↗
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↗
arXiv2006

Structural (B1 to B8) Phase Transition in MnO under Pressure: Comparison of All-electron and Pseudopotential Approaches

We employ the density functional theory to study a structural transition of MnO from B1 (rocksalt) to B8 (NiAs) structures that was observed experimentally at pressures around 100 GPa. We utilize all-electron description as well as norm-conserving pseudopotentials and demonstrate that these two approaches can significantly differ in quantitative predictions. We explicitly show that even small-core pseudopotentials exhibit transferability inaccuracies for quantities sensitive to the energy differences between high- and low-spin polarizations of valence electrons.

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↗
arXiv2006

Fermion nodes and nodal cells of noninteracting and interacting fermions

A fermion node is subset of fermionic configurations for which a real wave function vanishes due to the antisymmetry and the node divides the configurations space into compact nodal cells (domains). We analyze the properties of fermion nodes of fermionic ground state wave functions for a number of systems. For several models we demonstrate that noninteracting spin-polarized fermions in dimension two and higher have closed-shell ground state wave functions with the minimal two nodal cells for any system size and we formulate a theorem which sumarizes this result. The models include periodic fermion gas, fermions on the surface of a sphere, fermions in a box. We prove the same property for atomic states with up to 3d half-filled shells. Under rather general assumptions we then derive that the same is true for unpolarized systems with arbitrarily weak interactions using Bardeen-Cooper-Schrieffer (BCS) variational wave function. We further show that pair correlations included in the BCS wave function enable singlet pairs of particles to wind around the periodic box without crossing the node pointing towards the relationship of nodes to transport and many-body phases such as superconductivity. Finally, we point out that the arguments extend also to fermionic temperature dependent/imaginary-time density matrices. The results reveal fundamental properties of fermion nodal structures and provide new insights for accurate constructions of wave functions and density matrices in quantum and path integral Monte Carlo methods.

cond-mat.other↗
arXiv2006

Structure of fermion nodes and nodal cells

We study nodes of fermionic ground state wave functions. For 2D and higher we prove that spin-polarized, noninteracting fermions in a harmonic well have two nodal cells for arbitrary system size. The result extends to other noninteracting/mean-field models such as fermions on a sphere, in a periodic box or in Hartree-Fock atomic states. Spin-unpolarized noninteracting states have multiple nodal cells, however, interactions and many-body correlations generally relax the multiple cells to the minimal number of two. With some conditions, this is proved for interacting 2D and higher dimensions harmonic fermion systems of arbitrary size using the Bardeen-Cooper-Schrieffer variational wave function. Implications and extent of these results are briefly discussed.

cond-mat.other↗
arXiv2005

Electronic Structure and Origin of Ferromagnetism in CaB$_6$

Electronic structure calculations using quantum Monte Carlo (QMC) methods conclusively show that pure CaB$_6$ is a narrow-gap semiconductor with an $X$-point gap $\sim 1.3$ eV. This should put to rest controversies as to whether the compound is a semimetal or a semiconductor, as also theories suggesting it to be an excitonic insulator. Our extensive Hartree-Fock (HF) and density functional theory (DFT) calculations support the view that the hexaboride ferromagnetism can be induced by contamination with magnetic element atoms like Fe and that presence of La is not essential for this. La impurity, however, gives rise to a metallic state with a small electron-like Fermi surface as seen in ARPES experiments.

cond-mat.mtrl-sci↗