Chemistry Reference
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Fig. 8.19 Pictures for (a)a
ground state, (b) a doublon
state, (c) a holon state, and
(d) a doublon-holon pair state
a
Ground state
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8
b
Doublon
c
Holon
d
Doublon and holon
Eq. ( 8.22 ). In the case of the doublon, on the other hand, the movement by one unit
to the right needs the transfer of the down electron at this site to the right n. n. site.
Since our definition again needs no sign change, this also gives
t 0 . As a special
point of this model, the doublon and the hole never occupy the same site, because
the same occupation returns back the state to the ground state. We hence exclude
such N states to obtain the total N ( N 1) states.
At a glance, this model will give an impression that the picture is too simple,
because the particle motion inevitably rearranges the spin configuration in the
background. Furthermore, the frozen spin configurations would need some assump-
tion for averaging if we treat them independently. Meanwhile, this hamiltonian
exactly describes the charge part of the factorized eigenstate, which justifies our
analyses from here on [ 32 ].
The analytical treatment of this model is easy when we use a PBC and consider a
state with a total momentum, K , assuming the expression of
.
X
e iKl X
j
1 N
h l d lþj f ðjÞj
jfi
0
i :
(8.24)
l
By this analysis, it is found that (1) the exciton is formed when V is larger than
2 t 0 . This threshold value of V presents a sharp contrast to ordinary one-dimensional
cases, where infinitesimally small attraction forms a binding. The eigenstates of
K ¼ 0 and the associated optical conductivity spectrum are obtained as in
Fig. 8.20a . What attracts our attention most will be (2) the degeneracy between
the lowest exciton and the second lowest exciton. This feature is also unique to this
system, because the ordinary 1D systems never show such feature except for a case
 
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