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

References in corpus (8)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Quantum Critical Points and the Sign Problem
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Towards ab initio thermodynamics of the electron gas at strong degeneracy
• Prediction of a supersolid phase in high-pressure deuterium
• Path integral molecular dynamics simulations for Green's function in a system of identical bosons
• Path integral molecular dynamics for thermodynamics and Green's function of ultracold spinor bosons

Cited by in corpus (16)

• First principles simulations of dense hydrogen
• On the thermodynamics of fermions at any temperature based on parametrized partition function
• From Density Response to Energy Functionals and Back: An ab initio perspective on Matter Under Extreme Conditions
• Normal liquid ${}^3$He studied by Path Integral Monte Carlo with a parametrized partition function
• Quadratic Scaling Bosonic Path Integral Molecular Dynamics
• Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid
• 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