Theory of MMX-Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 239

lattice orders in the MMX compounds, extended H¨ckel band structure calculations
were first performed [ 12 - 14 ]. The Hartree-Fock approximation is applied to one-
dimensional, three-band [ 15 , 16 ] and two-band [ 17 , 18 ] extended Peierls-Hubbard
models. The Hartree-Fock calculations are extended to finite-temperature systems
[ 19 ]. These calculations miss quantum fluctuations that are inherent in one-
dimensional electron systems. Then, the quantum fluctuations originating from
electron correlation in these models have been quantitatively taken into account
by using the exact diagonalization method [ 20 , 21 ] and the quantum Monte Carlo
method [ 22 ]. In this chapter, we quantitatively treat the electron correlation in the
ground and excited states by using the exact diagonalization method and analyze
the numerical results with second- and fourth-order perturbation theories from the
strong coupling limit [ 23 ]. We discuss in detail the relevance of our theoretical
results to the experimentally observed variation of the ground and photoexcited
states. Dynamical processes during photoinduced transitions between the CDW
phase and the CP phase are also studied within the time-dependent Hartree-Fock
approximation [ 24 , 25 ].

12.2 Extended Peierls-Hubbard Model

To describe the ground- and excited-state properties, we adopt an extended
Peierls-Hubbard model, which is schematically shown in Fig. 12.2 . For simplicity,
it takes only M d z 2 orbitals into account. Their energy levels and transfer integrals
depend on the positions of the X ions,

X X

t MM ðc a;i;s c b;i;s þ ½t MXM aðy b;i þ y a;iþ 1 Þðc b;i;s c a;iþ 1 ;s þ H ¼ h.c :Þ h.c :Þ

i;s i;s

X

ðy a;i n a;i þ y b;i n b;i ÞþU M X
i

b ðn a;i;" n a;i;# þ n b;i;" n b;i;# Þ

i

X

ðV MM n a;i n b;i þ V MXM n b;i n a;iþ 1 ÞþV 2 X
i

þ ðn a;i n a;iþ 1 þ n b;i n b;iþ 1 Þ

i

X X

ðy 2

a;i þ y 2

2

þðK MX 2 = Þ

b;i ÞþðK MXM 2

= Þ ðy b;i þ y a;iþ 1 Þ ;

i i

(12.1)

where c a;i;s ðc b;i;s Þ at site a ( b ) in the i th binuclear

MM unit, h.c. denotes hermitian conjugate, n a;i;s ¼ c a;i;s c a;i;s ðn b;i;s ¼ c b;i;s c b;i;s Þ

creates an electron with spin s

is

the number operator, and n a;i ¼ S s n a;i;s ðn b;i ¼ S s n b;i;s Þ . The unit cell contains two

M sites a and b and an X site. The distance between the M site a ( b ) in the i th unit
and its neighboring X site, relative to that in the undistorted structure, is denoted by
y a , i ( y b , i ). Thus, the change in the distance between the i th and ( i + 1)th units is
given by y b , i + y a , i +1 . The nearest-neighbor transfer integral within the unit is fixed
at t MM . Meanwhile, the nearest-neighbor transfer integral through the X p z orbital,