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arXiv:2207.07653 · The Journal of Chemical Physics

Path integral molecular dynamics for thermodynamics and Green’s function of ultracold spinor bosons

Y. C. Yu, Shujuan Liu, Hongwei Xiong, Yunuo Xiong

Published Jul 14, 2022• 8 citations

Abstract

Most recently, the path integral molecular dynamics has been successfully used to consider the thermodynamics of single-component identical bosons and fermions. In this work, the path integral molecular dynamics is developed to simulate thermodynamics, Green's function, and momentum distribution of two-component bosons in three dimensions. As an example of our general method, we consider the thermodynamics of up to 16 bosons in a three-dimensional harmonic trap. For noninteracting spinor bosons, our simulation shows a bump in the heat capacity. As the repulsive interaction strength increases, however, we find the gradual disappearance of the bump in the heat capacity. We believe that this simulation result can be tested by ultracold spinor bosons with optical lattices and magnetic-field Feshbach resonance to tune the inter-particle interaction. We also calculate Green's function and momentum distribution of spinor bosons. Our work facilitates the exact numerical simulation of spinor bosons, whose property is one of the major problems in ultracold Bose gases.

DOI: 10.1063/5.0102460

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In this article we develop a general method to numerically calculate physical properties for a system of anyons with path integral molecular dynamics. We provide a unified method to calculate the thermodynamics of identical bosons, fermions and anyons. Our method is tested and applied to systems of anyons, bosons and fermions in a two-dimensional harmonic trap. We also consider a method to calculate the energy for fermions as an application of the path integral molecular dynamics to simulate the anyon model.

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Most recently, path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of identical bosons and fermions by B. Hirshberg et al.. In this work, we demonstrate that PIMD can be developed to calculate Green's function and extract momentum distribution for spin-polarized fermions. In particular, we show that the momentum distribution calculated by PIMD has potential application to numerous quantum systems, such as cold atom simulation of Mott insulator in Fermi-Hubbard model.

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.

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 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 properties as a function of this real parameter ξ, which provides the chance to calculate the thermodynamical properties of identical fermions by extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for ξ ≥ 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.