Chemistry Reference
In-Depth Information
3.0
S S
+
-
2.5
S S
0
0
STE
2.0
1.5
1.0
0.5
0.0
0
5
10
15
lo(site)
Fig. 8.14 Cross section of the two singlet potential surfaces at
DQ ΒΌ
1.0. Reprinted from
Iwano [
24
]
3.0
T2
2.5
S
3
+
S
S
S
S
S
S
S
S
0
+
+
-
-
S
2
2.0
+
0
0
0
T1
1.5
S1
1.0
0.5
0
0
30
5
10
15
20
25
lo (sites)
Fig. 8.15 Cross section of the adiabatic potential surfaces calculated by the DMRG calculation.
S
1,
S
2, and
S
3 are the first three excited states, while
T
1 and
T
2 are the first two triplet states
The readers might ask why we can distinguish the two types of solitons. Even
within this calculation, it is possible by inspecting the electronic density distribu-
tion in each state. Meanwhile, it is much clearer if we try a more advanced
calculation, that is, a DMRG calculation (K. Iwano, unpublished). In this method,
we can maintain the spin and spatial inversion symmetry almost perfectly, while in
the previous method the symmetries are not generally maintained except for some
cases like the regular CDW. The DMRG method enables us to separate singlet and
triplet states accurately, by which we are able to distinguish the soliton states. In
fact, we observe the degeneracy between
S
1 and
T
1 for a large
l
0
, which clearly
indicates that these are neutral solitons. As will be understood from Fig.
8.9
, the
neutral soliton has an unpaired spin, a pair of it having singlet and triplet states. It is
natural that they degenerate for a large soliton-soliton distance, since the effective
exchange coupling between them vanishes in the limit of a large distance. Mean-
while, we also notice a degeneracy between the
S
2 and
S
3 states. It is then naturally
interpreted as a charged-soliton pair, since a pair of it has the two choices of
S
+
S
and
S
S
+
.
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