A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem

Abstract

In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free from the fermion sign problem, enabling efficient simulations of fermionic systems. We found that by shifting the pseudo-fermion energy based on the energy of a non-interacting fermion system, we can efficiently and reliably infer the energy of fermionic systems in various situations, from strong quantum degeneracy to weak quantum degeneracy. We have performed first-principles simulations of quantum dots confined in a two-dimensional harmonic potential and found excellent agreement with benchmark results provided by other established methods. We believe that this pseudo-fermion propagator framework opens up new possibilities for first-principles simulations of fermionic systems.

30 pages, 9 figures

References in corpus (32)

• Many-Body Physics with Ultracold Gases
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Quantum phase transitions
• Fermi-Hubbard physics with atoms in an optical lattice
• The Hubbard Model
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
• A Constrained Path Monte Carlo Method for Fermion Ground States
• The Uniform Electron Gas at Warm Dense Matter Conditions
• Crossover from Fermi liquid to Wigner molecule behavior in quantum dots
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter
• Accurate exchange-correlation energies for the warm dense electron gas
• First principles simulations of dense hydrogen
• Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes
• Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature
• Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature
• Path Integral Molecular Dynamics for Fermions: Alleviating the Sign Problem with the Bogoliubov Inequality
• Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration
• On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem
• High-order Path Integral Monte Carlo methods for solving quantum dot problems
• Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
• Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions
• Exchange-correlation effect in the charge response of a warm dense electron gas
• On the thermodynamics of fermions at any temperature based on parametrized partition function
• Path-integral Monte Carlo worm algorithm for Bose systems with periodic boundary conditions
• Normal liquid ${}^3$He studied by Path Integral Monte Carlo with a parametrized partition function
• Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
• Performance of the coupled cluster singles and doubles method on two-dimensional quantum dots
• Accelerated free energy estimation in ab initio path integral Monte Carlo simulations
• Revisiting the properties of superfluid and normal liquid ${}^4$He using ab initio potentials
• GPU acceleration of ab initio simulations of large-scale identical particles based on path integral molecular dynamics