By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature <p>thermodynamic properties of fictitious identical particles with a real parameter ξ interpolating continuously between bosons (ξ=1) and fermions (ξ=-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 ξ, 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 ξ{greater than or equal to}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.
Path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of large bosonic systems in a recent study [Hirshberg et al., Proc. Natl. Acad. Sci. U. S. A. 116, 21445 (2019)]. In this work, we extend PIMD techniques to study Green’s function for bosonic systems. We demonstrate that the development of the original PIMD method enables us to calculate Green’s function and extract momentum distribution from our simulations. We also apply our method to systems of identical interacting bosons to study Berezinskii–Kosterlitz–Thouless transition around its critical temperature.
In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of large fermion systems with numerical simulation. As an example, we present energies for up to 50 noninteracting fermions and up to 20 interacting fermions at all temperatures and show good agreement with the analytical result for noninteracting case.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.