Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems

Abstract

Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and have been used in path integral Monte Carlo (PIMC) to accurately simulate warm dense matter with up to 1000 electrons (T. Dornheim et al., arXiv:2311.08098 (2023)). The inclusion of fictitious identical particles in path integral molecular dynamics (PIMD) can provide another way to simulate fermion systems. In a recent paper (J. Chem. Phys. 159, 154107 (2023)), Feldman and Hirshberg improved the recursive formula for PIMD of N identical bosons, significantly reducing the computational complexity from $O(P{N}^3)$ to $O(N^2+PN)$. 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 by using the recursive technique. As an example, we use the quadratic scaling PIMD for fictitious identical particles to study the simulation of hundreds of fermions in a two-dimensional periodic potential, in the hope of providing a simulation tool for two-dimensional Fermi-Hubbard model and other strongly correlated fermion systems, such as the simulation of ultracold fermionic gases in optical lattices.

arXiv comment30 pages, 8 figures

References in corpus (39)

• Many-Body Physics with Ultracold Gases
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Nearsightedness of Electronic Matter
• Fermi-Hubbard physics with atoms in an optical lattice
• The Hubbard Model
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
• BCS-BEC Crossover and the Unitary Fermi Gas
• The Uniform Electron Gas at Warm Dense Matter Conditions
• Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Ab initio thermodynamic results for the degenerate electron gas at finite temperature
• Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions
• The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter
• Density matrix quantum Monte Carlo
• Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
• Critical Temperature Curve in the BEC-BCS Crossover
• Path Integral Molecular Dynamics for Bosons
• Interaction Picture Density Matrix Quantum Monte Carlo
• Quantum Simulation of an Extended Fermi-Hubbard Model Using a 2D Lattice of Dopant-based Quantum Dots
• Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature
• Multilevel blocking approach to the fermion sign problem in path-integral Monte Carlo simulations
• Path integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Path Integral Molecular Dynamics for Fermions: Alleviating the Sign Problem with the Bogoliubov Inequality
• Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration
• Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations
• Restricted configuration path integral Monte Carlo
• Towards ab initio thermodynamics of the electron gas at strong degeneracy
• On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem
• Prediction of a supersolid phase in high-pressure deuterium
• Exchange-correlation effect in the charge response of a warm dense electron gas
• 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
• Path-integral Monte Carlo worm algorithm for Bose systems with periodic boundary conditions
• Quadratic Scaling Bosonic Path Integral Molecular Dynamics
• 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

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• 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
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem