Sign problem of the fermionic shadow wave function

On the Possibility of Helium Adsorption in Nitrogen Doped Graphitic Materials

The potassium salt of polyheptazine imide (K-PHI) is a promising photocatalyst for various chemical reactions. From powder X-ray diffraction data an idealized structural model of K-PHI has been derived. Using atomic coordinates of this model we defined an energetically optimized K-PHI structure, in which the K ions are present in the pore and between the PHI-planes. The distance between the anion framework and K+ resembles a frustrated Lewis pair-like structure, which we denote as frustrated Coulomb pair that results in an interesting adsorption environment for otherwise non-adsorbing, non-polar gas molecules. We demonstrate that even helium (He) gas molecules, which are known to have the lowest boiling point and the lowest intermolecular interactions, can be adsorbed in this polarized environment with an adsorption energy of  - 4.6 kJ mol-1 per He atom. The interaction between He atoms and K-PHI is partially originating from charge transfer, as disclosed by our energy decomposition analysis based on absolutely localized molecular orbitals. Due to very small charge transfer interactions, He gas adsorption saturates at 8 at%, which however can be subject to further improvement by cation variation.

Solving fermion problems without solving the sign problem: Symmetry-breaking wave functions from similarity-transformed propagators for solving two-dimensional quantum dots

It is well known that the use of the primitive second-order propagator in path-integral Monte Carlo calculations of many-fermion systems leads to the sign problem. This work will show that by using the similarity-transformed Fokker-Planck propagator, it is possible to solve for the ground state of a large quantum dot, with up to 100 polarized electrons, without solving the sign problem. These similarity-transformed propagators naturally produce rotational symmetry-breaking ground-state wave functions previously used in the study of quantum dots and quantum Hall effects. However, instead of localizing the electrons at positions that minimize the potential energy, this derivation shows that they should be located at positions that maximize the bosonic ground-state wave function. Further improvements in the energy can be obtained by using these as initial wave functions in a ground-state path-integral Monte Carlo calculation with second- and fourth-order propagators.

Metal-Insulator Transition of Solid Hydrogen by the Antisymmetric Shadow Wave Function

We revisit the pressure-induced molecular-atomic metal-insulator transition of solid hydrogen by means of variational quantum Monte Carlo simulations based on the antisymmetric shadow wave function. For the purpose of facilitating the study of the electronic structure of large-scale fermionic systems, the shadow wave function formalism is extended by a series of technical advancements as implemented in our HswfQMC code. Among others, these improvements include a revised optimization method for the employed shadow wave function and an enhanced treatment of periodic systems with long-range interactions. It is found that the superior accuracy of the antisymmetric shadow wave function results in a significantly increased transition pressure with respect to previous theoretical estimates.

Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid ^{4}He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional ^{4}He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form-a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid ^{3}He in three dimensions, improving previous variational and fixed-node energies.

Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction

We use the shadow wave function formalism as a convenient model to study the fermion sign problem affecting all projector quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary-time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results. Finally, we discuss the computational complexity of the fermion sign problem and methods for alleviating its severity.