Abstract
We present a practical analysis of the fermion sign problem in fermionic path integral Monte Carlo (PIMC) simulations in the grand-canonical ensemble (GCE). As a representative model system, we consider electrons in a 2D harmonic trap. We find that the sign problem in the GCE is even more severe than in the canonical ensemble at the same conditions, which, in general, makes the latter the preferred option. Despite these difficulties, we show that fermionic PIMC simulations in the GCE are still feasible in many cases, which potentially gives access to important quantities like the compressibility or the Matsubara Greens function. This has important implications for contemporary fields of research such as warm dense matter, ultracold atoms, and electrons in quantum dots.
Highlights
Having originally been introduced for the description of 4He in the 1960s [1, 2], the path integral Monte Carlo (PIMC) approach [3, 4, 5, 6] constitutes one of the most successful methods in statistical physics and related disciplines
All PIMC results in this work have been obtained using an implementation of the worm algorithm by Boninsegni et al [23, 24], which automatically operates in the grand-canonical ensemble (GCE)
Let us start our investigation with a verification of our implementation of the fermionic PIMC method in the GCE
Summary
Having originally been introduced for the description of 4He in the 1960s [1, 2], the path integral Monte Carlo (PIMC) approach [3, 4, 5, 6] constitutes one of the most successful methods in statistical physics and related disciplines. The PIMC method in principle allows to obtain quasi-exact results for quantum manybody systems at finite temperature without any empirical external input. We show that the GCE leads to a comparably more severe FSP, and to a potential sampling problem in the PIMC simulation due to the divergence of particle number distributions of bosons and fermions. The paper is organized as follows: in Sec. 2, we introduce the relevant theoretical background, including the PIMC method (2.1), the fermion sign problem (2.2), the grand-canonical ensemble (2.3), and the model system employed throughout this work (2.4).
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