On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem

Abstract

By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter $\xi$ interpolating continuously between bosons ($\xi =1$) and fermions ($\xi =-1$). Through general analysis and numerical experiments we find that the average energy may have good analytical property as a function of this real parameter $\xi$, which provides the chance to calculate the thermodynamical properties of identical fermions by an extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for $\xi \ge 0$. Using several examples, it is shown that our method can efficiently give accurate energy values for finite-temperature fermionic systems. Our work provides a chance to circumvent the fermion sign problem for some quantum systems.

24 pages, 7 figures, Accepted by The Journal of Chemical Physics

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• Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
• 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
• Revisiting the Fermion Sign Problem from the Structure of Lee-Yang Zeros. I. The Form of Partition Function for Indistinguishable Particles and Its Zeros at 0~K
• Periodic Boundary Conditions for Bosonic Path Integral Molecular Dynamics
• Dynamic properties of the warm dense uniform electron gas with the qSTLS dielectric scheme
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem
• Thermodynamics of free bosons and fermions in the hyperball
• Combining Harmonic Sampling with the Worm Algorithm to Improve the Efficiency of Path Integral Monte Carlo