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.
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.
Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and have been used in path integral Monte Carlo to accurately simulate warm dense matter with up to 1000 electrons [T. Dornheim et al., J. Phys. Chem. Lett. 15, 1305 (2024)1948-718510.1021/acs.jpclett.3c03193]. The inclusion of fictitious identical particles in path integral molecular dynamics (PIMD) can provide another way to simulate fermion systems. In a recent paper [Y. M. Y. Feldman et al., J. Chem. Phys. 159, 154107 (2023)0021-960610.1063/5.0173749], Feldman and Hirshberg improved the recursive formula for PIMD of identical bosons, significantly reducing the computational complexity. In this paper, we extend this latest recursive formula for bosons to PIMD of fictitious identical particles to improve the efficiency of simulating fermion systems. We also provide the virial estimator for calculating energy of fictitious identical particles by using the new recursive technique, which can help suppress fluctuations in energy calculation. As an example, we use the quadratic scaling PIMD for fictitious identical particles to study the simulation of hundreds and even thousands of fermions in a two-dimensional periodic potential, in the hope of providing a simulation tool for the large-scale Fermi-Hubbard model and other strongly correlated fermion systems, such as the simulation of ultracold fermionic gases in optical lattices and the extended Fermi-Hubbard model using quantum dots.
High Resolution Image Download MS PowerPoint Slide We combine the recent η-ensemble path integral Monte Carlo approach to the free energy [Dornheim et al. Phys. Rev. B 2025 111, L041114] with a recent fictitious partition function technique based on inserting a continuous variable that interpolates between the bosonic and Fermionic limits [Xiong and Xiong J. Chem. Phys. 2022 157, 094112] to deal with the Fermion sign problem. As a practical example, we apply our setup to the warm, dense, uniform electron gas over a broad range of densities and temperatures. We obtain accurate results for the exchange–correlation free energy down to half the Fermi temperature and find excellent agreement with the state-of-the-art parametrization by Groth et al. [ Phys. Rev. Lett. 2017 119, 135001]. Our work opens up new avenues for the future study of a host of interacting Fermi systems, including warm dense matter, ultracold atoms, and electrons in quantum dots, and for Fermionic free energy calculations with unprecedented system size.
The exchange antisymmetry between identical fermions gives rise to the well known fermion sign problem, in the form of large cancellation between positive and negative contribution to the partition function, making any simulation methods which directly sample this partition function exponentially difficult to converge. In this work, we employ path integral molecular dynamics (PIMD) and build upon the recently discovered fictitious particle model to investigate the fermion sign problem further. We consider the validity and invalidity condition for the method of parametrized path integral formulation of the partition function and extrapolation to circumvent the fermion sign problem. For the valid region of our method, our simulation shows that we may give accurate prediction of the energy for large fermion systems, which is much beyond the capability of the direct sampling in the traditional method. In particular, we find and verify a simple universal relation for high temperature noninteracting particles or strongly repulsive interacting particles at low temperatures.
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.
The exchange antisymmetry of identical fermions leads to an exponential computational bottleneck in ab initio simulations, known as the fermion sign problem. The thermodynamic approach of fictitious identical particles (Y. Xiong and H. Xiong, J. Chem. Phys. 157, 094112 (2022)) provides an efficient and accurate means to simulate some fermionic systems by overcoming the fermion sign problem. This method has been significantly promoted and used by National Ignition Facilities for the ab initio simulations and is believed to have wide application prospects in warm dense quantum matter (T. Dornheim et al., arXiv: 2402.19113 (2023)). By utilizing the fictitious identical particles in the bosonic regime and constant energy extrapolation method (Y. Xiong and H. Xiong, Phys. Rev. E 107, 055308 (2023); T. Morresi and G. Garberoglio, Phys. Rev. B 111, 014521 (2025)), there are promising results in simulating the energy of strongly quantum degenerate fermionic systems. The previous works mainly concern the energy of Fermi systems or only consider situations of weak quantum degeneracy. In this study, we extend the concept of the constant energy extrapolation method and demonstrate the potential of the constant density extrapolation method to accurately simulate the density distribution of fermionic systems in strongly quantum degenerate conditions. Furthermore, based on the energy derived from the constant energy extrapolation method, we present simulation results for the entropy of fermions.
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.