Path Integral Monte Carlo Method

In this chapter, we will give a review of the PIMC technique (Ceperley, 1995) and discuss all the necessary components required to build fermionic PIMC simulations. Starting from the thermal density, the path integral formalism will be introduced, a pair action method will be derived and the role of permuting paths in bosonic and fermionic systems will be explained. Then, the origin of the fermion sign problem will be discussed as well as the suggested solution based on the nodal surfaces of a trial density matrix (Ceperley, 1996,1991). Furthermore, a new time step analysis will be presented that studies the effect of the nodal action. Finally the distribution of permutation cycles from recent hydrogen simulations will be shown.

- The Thermal Density Matrix
- Imaginary Time Path Integrals
- Pair Density Matrix

- Path Integrals for Fermions and Bosons
- Monte Carlo Sampling

- Fermion Nodes

Burkhard Militzer 2003-01-15