# Solution of the 'sign problem' in pair approximation

## TL;DR

This paper introduces a novel Wigner function-based path integral Monte Carlo method that effectively addresses the fermionic sign problem by incorporating a pseudopotential accounting for Pauli blocking, enabling accurate calculations of Fermi systems.

## Contribution

A new quantum Monte Carlo approach using a phase-space Wigner representation with an effective pseudopotential to solve the fermionic sign problem.

## Key findings

- Good agreement with analytical Fermi distributions for ideal systems
- Explicit pseudopotential accounts for Pauli blocking effects
- Method applicable to strongly coupled Fermi systems in progress

## Abstract

The main difficulty for path integral Monte Carlo studies of Fermi systems results from the requirement of antisymmetrization of the density matrix and is known in literature as the 'sign problem'. To overcome this issue the new numerical version of the %{\large {\tiny {\Huge }}} Wigner approach to quantum mechanics for treatment thermodynamic properties of degenerate systems of fermions has been developed. The new path integral representation of quantum Wigner function in the phase space has been obtained for canonical ensemble. Explicit analytical expression of the Wigner function accounting for Fermi statistical effects by effective pair pseudopotential has been proposed. Derived pseudopotential depends on coordinates, momenta and degeneracy parameter of fermions and takes into account Pauli blocking of fermions in phase space. The new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been proposed. To test the developed approach calculations of the momentum distribution function of the degenerate ideal system of Fermi particles has been carried out in a good agreement with analytical Fermi distributions. Generalization of this approach for studies influence of interparticle interaction on momentum distribution functions of strongly coupled Fermi system is in progress.