Path-integral–expanded-ensemble Monte Carlo method in treatment of the sign problem for fermions

Abstract

Expanded-ensemble Monte Carlo method with Wang-Landau algorithm was used for calculations of the ratio of partition functions for classes of permutations in the problem of several interacting quantum particles (fermions) in an external field. Simulations for systems consisting of 2 up to 7 interacting particles in harmonic or Coulombic field were performed. The presented approach allows one to carry out calculations for low enough temperatures that makes it possible to extract data for the ground-state energy and low-temperature thermodynamics.

The uniform electron gas at warm dense matter conditions

“…In particular, we introduce the Metropolis algorithm [269], which constitutes the backbone of all subsequent path inegral Monte Carlo methods except the density matrix QMC paradigm. Not mentioned are the multilevel blocking idea by Mak, Egger and coworkers [270,271,272,273,274] and the expanded-ensemble approach by Vorontsov-Velyaminov et al [275,276].…”

Fermion sign problem in path integral Monte Carlo simulations: Quantum dots, ultracold atoms, and warm dense matter

“…( 1)] leads to a near cancellation of positive and negative terms both with decreasing temperature and increasing the system size [34]. This issue is commonly known as the fermion sign problem (FSP) [35][36][37][38], and generally prevents fermionic PIMC simulations once quantum degeneracy effects start to get important [39]. This is very unfortunate, as correlated Fermi systems offer a wealth of interesting effects such as the BCS-BEC crossover [43][44][45] in ultracold atoms and the formation of Wigner molecules in quantum dots [46][47][48].…”

Path integral molecular dynamics for bosons

“…Each term is weighted by the number of different permutations which lead to the same configuration. This observation has been used recently in attempts to overcome the Fermion sign problem in PIMC simulations [18,25]. For Bosons, all configurations give a positive contribution and no such sign problem arises.…”