Path Integral Molecular Dynamics for Fermions: Alleviating the Sign Problem with the Bogoliubov Inequality

Abstract

We present a method for performing path integral molecular dynamics (PIMD) simulations for fermions and address its sign problem. PIMD simulations are widely used for studying many-body quantum systems at thermal equilibrium. However, they assume that the particles are distinguishable and neglect bosonic and fermionic exchange effects. Interacting fermions play a key role in many chemical and physical systems, such as electrons in quantum dots and ultracold trapped atoms. A direct sampling of the fermionic partition function is impossible using PIMD since its integrand is not positive definite. We show that PIMD simulations for fermions are feasible by employing our recently developed method for bosonic PIMD and reweighting the results to obtain fermionic expectation values. The approach is tested against path integral Monte Carlo (PIMC) simulations for up to 7 electrons in a two-dimensional quantum dot for a range of interaction strengths. However, like PIMC, the method suffers from the sign problem at low temperatures. We propose a simple approach for alleviating it by simulating an auxiliary system with a larger average sign and obtaining an upper bound to the energy of the original system using the Bogoliubov inequality. This allows fermions to be studied at temperatures lower than would otherwise have been feasible using PIMD, as demonstrated in the case of a three-electron quantum dot. Our results extend the boundaries of PIMD simulations of fermions and will hopefully stimulate the development of new approaches for tackling the sign problem.

References in corpus (18)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Nuclear quantum effects enter the mainstream
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Single-atom imaging of fermions in a quantum-gas microscope
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• The Complex Langevin method: When can it be trusted?
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter
• Excitation spectrum of two correlated electrons in a lateral quantum dot with negligible Zeeman splitting
• Path Integral Molecular Dynamics for Bosons
• Multilevel blocking approach to the fermion sign problem in path-integral Monte Carlo simulations
• Discovering correlated fermions using quantum Monte Carlo
• Calculation of thermodynamic properties of finite Bose-Einstein systems
• High-dimensional neural network potentials for solvation: The case of protonated water clusters in helium
• Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement
• Transition to metallization in warm dense helium-hydrogen mixtures using stochastic density functional theory within the Kubo-Greenwood formalism
• Quantum symmetry from enhanced sampling methods
• Path Integral Density Functional Theory

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