The one body density matrix (OBDM) of a homogeneous system described by the
many body wave function
according to (1.18) is equal
to
Since in DMC calculation does not sample directly the ground-state probability
distribution , but instead the mixed probability
(2.12)
one obtains the mixed one-body density matrix as the output
This formula can be rewritten in a way convenient for the Monte Carlo sampling:
![]() |
(2.142) |
In order to gain better statistics it is convenient to average over all possible
pairs of particles
![]() |
(2.143) |
The asymptotic limit of the OBDM gives the condensate density
![]() |
(2.144) |
![]() |
(2.145) |