Chemistry Reference
In-Depth Information
the momentum distribution can be obtained by Fourier transforming
r
ij
. The
real-space density of several example systems is shown in Figure 14. These
plots show the development with increasing density of a shell-type structure
with insulator phases visible as plateaus at integer local density. Specifically,
system (a) is in the superfluid phase. If the Hubbard interaction
U
is raised
to about the critical value of the superfluid-insulator transition [system (b)],
n
n
(b)
(a)
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
r a
r
a
0
2
4
6
0
5
10
/
/
n
n
(c)
(d)
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
r a
r
a
0
2
4
6
0
5
10
/
/
n
n
(e)
(f)
2
1.5
1.5
1
1
0.5
0.5
r a
r a
0
2
4
6
8
0
5
10
/
/
Figure 14
Superfluid-insulator transition in an optical lattice: Particle density (per
lattice site) as a function of distance from the trap center for various parameters and
filling factors. (Taken with permission from Ref. 111.)
