PATH-INTEGRAL MONTE-CARLO METHOD IN QUANTUM STATISTICS FOR A SYSTEM OF N IDENTICAL FERMIONS

A rigorous expression for the partition function of N identical fermions with spin 1/2 is obtained in a form suitable for a path-integral Monte Carlo (PIMC) simulation of a many-electron system at a finite temperature. A sum over permutations is reduced to a sum over classes with readily determinable factors. A distribution over projections and values of the total spin is also obtained, enabling PIMC calculations of spin-dependent quantities. A MC algorithm is proposed which accounts simultaneously for all types of trajectory linkages. A test calculation, four electrons in a spherical cavity with a radius of 1 nm at a temperature of 300-2000 K, is performed.