The feasibility of using Monte Carlo methods in finite fermion systems has been investigated. The basic tool is a (recently suggested) functional integral representation of $Z=\mathrm{tr}[\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}II)]$ using real coherent states of Slater determinants. Conditions for using the discretized ( $N$ -point lattice) version as a starting point for Monte Carlo integrations are studied. The limit of large $\ensuremath{\beta}$ is achieved only with large $\ensuremath{\surd}N$. For a two-fermion system numerical calculations of the ground-state energy agree farily well with the exact value.The feasibility of using Monte Carlo methods in finite fermion systems has been investigated. The basic tool is a (recently suggested) functional integral representation of $Z=\mathrm{tr}[\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}II)]$ using real coherent states of Slater determinants. Conditions for using the discretized ($N$-point lattice) version as a starting point for Monte Carlo integrations are studied. The limit of large $\ensuremath{\beta}$ is achieved only with large $\ensuremath{\surd}N$. For a two-fermion system numerical calculations of the ground-state energy agree farily well with the exact value.

Physical Review LettersApr 18, 19839 citations

Quantum-Monte-Carlo simulations for fermionic systems

I. Morgenstern

The European Physical Journal BJun 1, 198914 citations

Path-integral Monte Carlo method in quantum statistics for a system ofNidentical fermions

Alexander P. Lyubartsev, P. N. Vorontsov‐Velyaminov

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. An 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.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. An 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.

Physical Review ADec 1, 199338 citations

A proposal for Monte Carlo simulations of fermionic systems

Francesco Fucito, Enzo Marinari, Giorgio Parisi A +1 more

Nuclear Physics BMay 1, 1981291 citations

N

-point lattice) version as a starting point for Monte Carlo integrations are studied. The limit of large $\ensuremath{\beta}$ is achieved only with large $\ensuremath{\surd}N$. For a two-fermion system numerical calculations of the ground-state energy agree farily well with the exact value.