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To account for the interference effects of the Coulomb and exchangeinteractions of electrons a new path integral representation of the densitymatrix has been developed in the canonical ensemble at finite temperatures. Thedeveloped representation allows to reduce the notorious ``fermionic signproblem'' in the Monte Carlo simulations of fermionic systems. The obtainedresults for pair distribution functions in plasma and uniform electron gasdemonstrate the short-range quantum ordering of electrons associated withexchange excitons in the literature. This fine physical effect was not observedearlier in standard path integral Monte Carlo simulations.

Monte Carlo simulations of the electron short-range quantum ordering in Coulomb systems: Reducing the "fermionic sign problem"