Properties of fermionic systems with the Path-integral ground state method

Abstract

We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure ${}^4$He systems demonstrate most of the features of the method. Complementarily, for pure ${}^3$He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate ${}^3$He-${}^4$He mixtures, demonstrating the method's robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature $T=0$ without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the ${}^3$He kinetic energy in the mixture.

40 pages, 11 figures

References in corpus (19)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Quantum Machine Learning for Chemistry and Physics
• Nuclear and neutron-star matter from local chiral interactions
• Quantum deep field: data-driven wave function, electron density generation, and atomization energy prediction and extrapolation with machine learning
• Exact ground state Monte Carlo method for Bosons without importance sampling
• Ionic polaron in a Bose-Einstein condensate
• Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
• Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo
• Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum
• Finite-range effects in the unitary Fermi polaron
• Particle partition entanglement of bosonic Luttinger liquids
• Kinetic energy and momentum distribution of isotopic liquid helium mixtures
• Quantum Coherent States of Interacting Bose-Fermi Mixtures in One Dimension
• The Momentum Distribution of Liquid ${}^3$He
• Weakly parametrized Jastrow ansatz for a strongly correlated Bose system
• Weighted nodal domain averages of eigenstates for quantum Monte Carlo and beyond
• Performance of adiabatic melting as a method to pursue the lowest possible temperature in ${}^3$He and ${}^3$He-${}^4$He mixture at the ${}^4$He crystallization pressure
• Neural-Network Quantum States for Periodic Systems in Continuous Space