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Taylor series perspective on ab initio path integral Monte Carlo simulations with Fermi-Dirac statistics

Tobias Dornheim1,2,*, Alexander Benedix Robles2,1,3, Paul Hamann1,4,2, Thomas M. Chuna2,1, Pontus Svensson1,2, Sebastian Schwalbe1,2, Zhandos A. Moldabekov1,2, Panagiotis Tolias5, and Jan Vorberger1

  • *Contact author: t.dornheim@hzdr.de
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Phys. Rev. Research 8, 023042 – Published 13 April, 2026

DOI: https://doi.org/10.1103/53fr-mnm6

Abstract

The fermion sign problem constitutes a fundamental computational bottleneck across a plethora of research fields in physics, quantum chemistry, and related disciplines. Recently, it has been suggested to alleviate the sign problem in ab initio path integral molecular dynamics and path integral Monte Carlo (PIMC) calculations based on the simulation of fictitious identical particles that are represented by a continuous quantum statistics variable ξ [Xiong and Xiong, J. Chem. Phys. 157, 094112 (2022)]. This idea facilitated a host of applications including the interpretation of an x-ray scattering experiment with strongly compressed beryllium at the National Ignition Facility [Dornheim et al., Nat. Commun. 16, 5103 (2025)]. In the present work, we express the original isothermal ξ extrapolation method as a special case of a truncated Taylor series expansion around the ξ=0 limit of distinguishable particles. We derive PIMC estimators that allow us to evaluate the Taylor coefficients up to arbitrary order and we carry out extensive PIMC simulations of the warm dense electron gas to systematically analyze the sign problem from this perspective. This gives us important insights into the applicability of the ξ extrapolation method for different levels of quantum degeneracy in terms of the Taylor series radius of convergence. Moreover, the direct PIMC evaluation of the ξ derivatives, in principle, removes the necessity for simulations at different values of ξ and can facilitate more efficient simulations that are designed to maximize compute time in those regions of the full permutation space that contribute most to the final Taylor estimate of the fermionic expectation value of interest.

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Phys. Rev. Research 8, 023042– Published 13 April, 2026
  • Received 14 September 2025
  • Accepted 25 February 2026
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