Computational Physics

408 Quantum Monte Carlo methods

0 0.5 1 1.5 2 2.5 3 3.5 4

V

r

Figure 12.5. The cumulant potential for

τ=0.2 (diamonds) and the Coulomb

potential. It is clearly seen that the cumulant potential is rounded off atr=0.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6 7 8

r

Figure 12.6. PIMC ground state amplitude|ψ(r)|^2 (diamonds) and the exact result.

Sixty thousand Monte Carlo sweeps with a chain length of 100 andτ=0.2 were

used.

particles; rather, a collection of atoms is considered, interacting through Lennard–
Jones potentials. We shall not go into details of implementation and phase diagram,
but refer to the work by Ceperley and Pollock [ 3 , 4 ].

12.4.3 Increasing the efficiency

The local structure of the action enables us to use the heat-bath algorithm instead
of the classical sampling rule, in which particles are displaced at random uniformly