Non-linear biases, stochastically-sampled effective Hamiltonians and spectral functions in quantum Monte Carlo methods

In this article we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of non-linear expectation values, and approaches by which these errors can be corrected. We begin with a study of the Krylov-projected FCIQMC (KP-FCIQMC) approach, which was recently introduced to allow efficient, stochastic calculation of dynamical properties. This requires the solution of a sampled effective Hamiltonian, resulting in a non-linear operation on these stochastic variables. We investigate the probability distribution of this eigenvalue problem to study both stochastic errors and systematic biases in the approach, and demonstrate that such errors can be significantly corrected by moving to a more appropriate basis. This is lastly expanded to include consideration of the correlation function QMC approach of Ceperley and Bernu, showing how such an approach can be taken in the FCIQMC framework.Comment: 12 pages, 7 figure

Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure

Presence of Visceral Larva Migrans in the Urinary Bladder of a Woman in Khorramabad, Iran

The presence of Visceral Larva Migrans (VLM) in a patient is reported. A 57-year- old woman suffering from right upper abdominal and suprapubic pain referred into a clinic in Khorramabad, Lorestan Province, Iran. A cystoscopy was performed and biopsy was taken. The light microscopic study showed a couple of larvae as well as mononuclear inflammatory cell- infiltration. Because occurrence of VLM is potentially problem in rural areas, it is recommended that an educational program to be initiated to prevent and control VLM infection in both rural and urban people. Clinicians also should consider the clinical features of visceral larva migrans

Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformations

© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller correlator leads to a non-Hermitian effective Hamiltonian, which can be expressed exactly in momentum-space representation and contains three-body interactions. We apply this methodology to study the two-dimensional Hubbard model with repulsive interactions near half filling in the intermediate interaction strength regime (U/t=4). We show that at optimal or near optimal strength of the Gutzwiller correlator, the similarity-transformed Hamiltonian has extremely compact right eigenvectors, which can be sampled to high accuracy using the full configuration interaction quantum Monte Carlo (FCIQMC) method and its initiator approximation. Near-optimal correlators can be obtained using a simple projective equation, thus obviating the need for a numerical optimization of the correlator. The FCIQMC method, as a projective technique, is well suited for such non-Hermitian problems, and its stochastic nature can handle the three-body interactions exactly without undue increase in computational cost. The highly compact nature of the right eigenvectors means that the initiator approximation in FCIQMC is not severe and that large lattices can be simulated, well beyond the reach of the method applied to the original Hubbard Hamiltonian. Results are provided in lattice sizes up to 50 sites and compared to auxiliary-field QMC. New benchmark results are provided in the off-half-filling regime, with no severe sign problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy

Convergence of many-body wavefunction expansions using a plane wave basis: from the homogeneous electron gas to the solid state

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete basis set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple analytic and numerical results from second-order M{\o}ller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis set truncation when constructing many-electron wavefunctions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wavefunction methods, from MP2 to coupled-cluster doubles theory (CCD) and the random-phase approximation plus second-order screened exchange (RPA+SOSEX). Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane wave basis and thereby allow application of these methods to more realistic physical problems.Comment: 15 pages, 9 figure

Regional differences in the coupling between resting cerebral blood flow and metabolism may indicate action preparedness as a default state.

Although most functional neuroimaging studies examine task effects, interest intensifies in the "default" resting brain. Resting conditions show consistent regional activity, yet oxygen extraction fraction constancy across regions. We compared resting cerebral metabolic rates of glucose (CMRgl) measured with 18F-labeled 2-fluoro-2-deoxy-D-glucose to cerebral blood flow (CBF) 15O-H2O measures, using the same positron emission tomography scanner in 2 samples (n = 60 and 30) of healthy right-handed adults. Region to whole-brain ratios were calculated for 35 standard regions of interest, and compared between CBF and CMRgl to determine perfusion relative to metabolism. Primary visual and auditory areas showed coupling between CBF and CMRgl, limbic and subcortical regions--basal ganglia, thalamus and posterior fossa structures--were hyperperfused, whereas association cortices were hypoperfused. Hyperperfusion was higher in left than right hemisphere for most cortical and subcallosal limbic regions, but symmetric in cingulate, basal ganglia and somatomotor regions. Hyperperfused regions are perhaps those where activation is anticipated at short notice, whereas downstream cortical modulatory regions have longer "lead times" for deployment. The novel observation of systematic uncoupling of CBF and CMRgl may help elucidate the potential biological significance of the "default" resting state. Whether greater left hemispheric hyperperfusion reflects lateral dominance needs further examination