Lowering of the kinetic energy in interacting quantum systems

Fermionic physics from ab initio path integral Monte Carlo simulations of fictitious identical particles

The ab initio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion sign problem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the sign problem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the sign problem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

Momentum distribution function and short-range correlations of the warm dense electron gas: Ab initio quantum Monte Carlo results

In a classical plasma the momentum distribution, n(k), decays exponentially, for large k, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay, n_{∞}(k)∼k^{-8} has been predicted. This is of relevance for cross sections and threshold processes in dense plasmas that depend on the number of energetic particles. Here we present extensive ab initio results for the momentum distribution of the nonideal uniform electron gas at warm dense matter conditions. Our results are based on first principle fermionic path integral Monte Carlo (CPIMC) simulations and clearly confirm the k^{-8} asymptotic. This asymptotic behavior is directly linked to short-range correlations which are analyzed via the on-top pair distribution function (on-top PDF), i.e., the PDF of electrons with opposite spin. We present extensive results for the density and temperature dependence of the on-top PDF and for the momentum distribution in the entire momentum range.

Direct linear term in the equation of state of plasmas

We discuss a long-standing discrepancy in the equation of state of charge-neutral plasmas, the occurrence of an e(2) direct term. This e(2) term may appear in dependence of the way to determine the mean value of the potential energy. We show that such a contribution should not appear for pure Coulomb interaction.

Momentum distribution of the homogeneous electron gas

We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 calculations concerning quasiparticle properties over a broad density region (1≤r(s)≲10) and show that, near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.

Efficient implementation of the Hellmann-Feynman theorem in a diffusion Monte Carlo calculation

Kinetic and potential energies of systems of (4)He atoms in the solid phase are computed at T = 0. Results at two densities of the liquid phase are presented as well. Calculations are performed by the multiweight extension to the diffusion Monte Carlo method that allows the application of the Hellmann-Feynman theorem in a robust and efficient way. This is a general method that can be applied in other situations of interest as well.

Density of phonon states in solid parahydrogen from inelastic neutron scattering

We have measured the inelastic neutron scattering spectrum of solid parahydrogen (at low pressure and T=13.3 K) using the thermal original spectrometer with cylindrical analyzers spectrometer at the ISIS pulsed neutron source (UK). From the experimental spectrum we have obtained the parahydrogen density of phonon states which has been compared with the estimates available in the literature. The present determination improves substantially the previous experimental scenario from the point of view of both statistics and accuracy. The comparison with the most recent estimate obtained from a quantum mechanical simulation of the molecular dynamics calls for an improvement of the computational methods..