Path integral molecular dynamics simulations for Green’s function in a system of identical bosons

2022

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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, e.g. ultracold fermionic atoms in optical lattices.

“…Similarly to Green's function for bosons in our previous work 22 , we may consider the following partition function for Green's function…”

Section: Pimd For Green's Function and Momentum Distributionmentioning

confidence: 99%

Section: Pimd For Green's Function and Momentum Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…is the potential function for bosons 20,22 , which can be obtained from Eqs. (8) and ( 9) without considering the factor (−1) k in Eq.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Numerical calculation of Green’s function and momentum distribution for spin-polarized fermions by path integral molecular dynamics

Yunu

2022

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

Yongle

Liu

et al. 2022

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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 the 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 sixteen 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 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.

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

2022

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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.