Theory of MX Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 128

Fig. 8.17 Excitation
spectrum of two spinon
excitations

2.0

2 Jsin(Q/2)

π

1.5

Spinon
Conituum

1.0

0.5 π Jsin(Q)

0.0

0.0 0.5 1.0 1.5 2.0

Q/ π

is now in progress at J-PARC. In Fig. 8.17 , we sketch a simple expectation for the
magnetic excitations.

8.3.2 Optical Properties

The optical conductivity spectrum of the Ni system was first observed by Okamoto
et al. [ 28 ]. It consisted of a dominant sharp main peak, which suggested the role of
the exciton effect. We already discussed the exciton effect in the CDW system.
Although the simple treatment in the previous section cannot be applied, the
physical meaning is not essentially different even in this strongly correlated system.
By the way, we were not so surprised by this exciton-like feature from the analogy
to the Pt system, of which the spectrum had been known to have the same feature.
What rather attracted our attention was a long tail extending to higher energies.
Because we lacked enough knowledge about the optical properties of strongly
correlated systems at that time, there was no clear answer to that.
Before this finding, the spectra in other strongly correlated systems had been
obtained. For instance, those of undoped cuprates, which were also Mott insulators,
were known at that time. Their features were that they had no features, although this
might sound paradoxical. In fact, their spectral shapes were broad band-like ones
and simply interpreted to originate from its two-dimensional nature, namely, a
relatively weak e-h binding.
In 2000, Jeckelmann calculated the optical conductivity spectrum of the one-
dimensional Hubbard model for the first time [ 29 ]. While his model was not the
extended Hubbard model, the long-tail feature was reproduced clearly. His method
was based on a dynamical DMRG (DDMRG) and this became the first study that
demonstrated the power of this method. According to this calculation, the above-
mentioned long tail is mainly due to an unique type of dispersion of a
doublon-holon pair. As is explained in detail below, a doublon and a holon
correspond to the electron and the hole, respectively, in band insulators including
the CDW insulator. In this sense, multielectron excitations that occur near the