By adding disorder to the system the condensate and superfluid
density are depleted. One expects that at some critical amount of
disorder superfluidity vanishes and the system becomes normal. We
want to investigate the quantum phase transition of the hard-sphere
gas in the presence of hard-sphere impurities at .
In the vicinity of the phase transition the correlation length becomes
large. This means that in the MC simulation one has finite size
errors (see 3.4.3) and it is necessary to carry
out calculations with systems of different size and finally
extrapolate to the thermodynamic limit.
We calculate the superfluid density as a function of the
concentration of impurities while keeping the size of the
impurity constant. The simulation is carried out for systems of 16,
32 and 64 particles with periodic boundary conditions. The results
for the low density
is presented in
Fig. 4.10 and for the density
in
Fig. 4.11.
Figure 4.10:
Superfluid density measured as a function of
at density
and with 16, 32 and 64
particles in the simulation box
Figure 4.11:
Superfluid density measured as a function of
at density
and with 16, 32 and 64
particles in the simulation box
The figures show that there is no significant finite size effect
present which means that we are still far from the critical region.
The further increase of the strength of
disorder in Fig. 4.10 and Fig. 4.10
is impossible, because
of the constraint of non-overlapping impurities.
We conclude that within our model of non-overlapping impurities
the superfluid-insulator quantum transition is absent.
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