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.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.

arXiv:2104.10032Journal of Physics A Mathematical and TheoreticalJul 14, 202134 citations

Green functions in the microcanonical ensemble

G.D. White, Philip John Siemens

Jan 1, 19850 citations

Resolution of the Hierarchy of Green's Functions for Fermions

Shigeji Fujita

The rigorous evolution equations for the one-body Green's functions ( ${g}^{>},{g}^{<}$ ) describing a system of interacting fermions are not closed (an analog of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for many-body distribution functions). The analysis of these equations is made in terms of proper connected diagrams. It is established that in the bulk limit, $N$ (particle number) $\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\Omega}$ (volume) $\ensuremath{\rightarrow}\ensuremath{\infty}$ while $\frac{N}{\ensuremath{\Omega}}$ remains finite, these equations can rigorously be transformed into closed equations with respect to ( ${g}^{>},{g}^{<}$ ).The rigorous evolution equations for the one-body Green's functions (${g}^{>},{g}^{<}$) describing a system of interacting fermions are not closed (an analog of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for many-body distribution functions). The analysis of these equations is made in terms of proper connected diagrams. It is established that in the bulk limit, $N$ (particle number) $\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\Omega}$ (volume) $\ensuremath{\rightarrow}\ensuremath{\infty}$ while $\frac{N}{\ensuremath{\Omega}}$ remains finite, these equations can rigorously be transformed into closed equations with respect to (${g}^{>},{g}^{<}$).

Physical Review ASep 1, 197128 citations

The canonical ensemble revisited: a projection operator approach

Wim Magnus, F. Brosens

Bulletin of the American Physical SocietyMar 18, 20160 citations

The rigorous evolution equations for the one-body Green's functions (

{g}^{>},{g}^{<}

) describing a system of interacting fermions are not closed (an analog of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for many-body distribution functions). The analysis of these equations is made in terms of proper connected diagrams. It is established that in the bulk limit,

N

(particle number) $\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\Omega}$ (volume) $\ensuremath{\rightarrow}\ensuremath{\infty}$ while $\frac{N}{\ensuremath{\Omega}}$ remains finite, these equations can rigorously be transformed into closed equations with respect to (

{g}^{>},{g}^{<}