Electron correlations in narrow energy bands: ground state energy and metal-insulator transition
The electron correlations in narrow energy bands are examined within the framework of the Hubbard model. The single-particle Green function and energy spectrum are obtained in a paramagnetic state at half-filling by means of a new two-pole approximation. Analytical expressions for the energy gap,...
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Інститут фізики конденсованих систем НАН України
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| Цитувати: | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition / L. Didukh, Yu. Skorenkyy // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 787-798. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859709652427603968 |
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| author | Didukh, L. Skorenkyy, Yu. |
| author_facet | Didukh, L. Skorenkyy, Yu. |
| citation_txt | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition / L. Didukh, Yu. Skorenkyy // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 787-798. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | The electron correlations in narrow energy bands are examined within the
framework of the Hubbard model. The single-particle Green function and
energy spectrum are obtained in a paramagnetic state at half-filling by
means of a new two-pole approximation. Analytical expressions for the energy gap, polar states concentration and energy of the system are found in
the ground state. Metal-insulator transitions in the model at the change of
bandwidth or temperature are investigated. The results obtained are used
for interpretation of some experimental data in narrow-band materials.
В данiй роботi електроннi кореляцiї у вузьких енергетичних зонах
вивчаються в рамках моделi Габбарда. За допомогою нового двополюсного наближення знайдено одночастинкову функцiю Грiна та
енергетичний спектр у парамагнiтному станi при половинному заповненнi. В основному станi знайдено аналiтичнi вирази для ширини енергетичної щiлини, концентрацiї полярних станiв та енергiї системи. Дослiджено переходи метал-дiелектрик при змiнi ширини зони та при змiнi температури. Отриманi результати використанi для iнтерпретацiї деяких експериментальних даних для вузькозонних матерiалiв.
|
| first_indexed | 2025-12-01T04:37:29Z |
| format | Article |
| fulltext |
Condensed Matter Physics, 2000, Vol. 3, No. 4(24), pp. 787–798
Electron correlations in narrow energy
bands: ground state energy and
metal-insulator transition
L.Didukh∗, Yu.Skorenkyy
Ternopil State Technical University, Department of Physics,
56 Rus’ka Str., 46001 Ternopil, Ukraine
Received May 5, 2000, in final form October 28, 2000
The electron correlations in narrow energy bands are examined within the
framework of the Hubbard model. The single-particle Green function and
energy spectrum are obtained in a paramagnetic state at half-filling by
means of a new two-pole approximation. Analytical expressions for the en-
ergy gap, polar states concentration and energy of the system are found in
the ground state. Metal-insulator transitions in the model at the change of
bandwidth or temperature are investigated. The results obtained are used
for interpretation of some experimental data in narrow-band materials.
PACS: 71.28.+d, 71.27.+a, 71.10.Fd, 71.30.+h
Key words: narrow energy bands, Hubbard Hamiltonian, metal-insulator
transition, ground state energy
1. Introduction
Among the metal-insulator transitions (MIT) observed in narrow-band materials
of great interest are the transitions from paramagnetic metal state to paramagnetic
insulator state at the increase of temperature exhibited by the systems NiS2−xSex [1–
3], (V1−xCrx)2O3 [1,4] and Y1−xCaxTiO3 [5,6]; in these systems the paramagnetic
insulator – paramagnetic metal transitions under external pressure are observed as
well. There are reasons to believe that the mentioned transitions are caused by the
electron-electron interactions and can be described within the framework of Hubbard
model [7].
Hubbard model is the simplest model describing MIT in the materials with nar-
row energy bands. This model describes a single non-degenerate band of electrons
with the local Coulomb interaction. The model Hamiltonian contains two energy
parameters: the hopping integral of an electron from one site to another and the
∗E-mail: didukh@tu.edu.te.ua, Tel.:+380352251946, Fax: +380352254983
c© L.Didukh, Yu.Skorenkyy 787
L.Didukh, Yu.Skorenkyy
intraatomic Coulomb repulsion of two electrons of the opposite spins. This model is
used intensively (for recent reviews see [1,8–10]) in order to describe the peculiari-
ties of physical properties of narrow-band materials; in this connection two-pole ap-
proaches seem to be attractive. The two-pole approaches in the Hubbard model and
the Hubbard bands conception (being caused by the two-pole approximation) have
been useful in understanding the peculiarities of electric and magnetic properties of
narrow-band materials [1,10]. However within the framework of two-pole approaches
there is a number of issues, in particular the problem of describing metal-insulator
transitions [10,14–21].
In the present paper, the recently proposed two-pole approximation [11] is used
to study the effects of electron correlations in the Hubbard model. The single parti-
cle Green function and the energy spectrum are obtained. Analytical dependencies
of the energy gap, polar states (doublons or holes) concentration and the energy of
the system on the model parameters are found in the ground state. Dependencies
for the energy gap, polar states concentration on temperature are calculated. The
results obtained are compared with the corresponding results of other approxima-
tions and are used for the interpretation of some experimental data. In particular,
the observable transitions from an insulating state to a metallic state at the increase
of a bandwidth, and from a metallic state to an insulating state at the increasing
temperature are explained.
2. Single-particle Green function and energy spectrum
The Hubbard Hamiltonian [1] in terms of transition-operators of i-site from state
|l〉 to state |k〉 Xkl
i [12] is written as
H = H0 +H1 +H ′
1; (2.1)
H0 = −µ
∑
iσ
(
Xσ
i +X2
i
)
+ U
∑
i
X2
i , (2.2)
H1 =
∑
ijσ,i 6=j
tij
(
Xσ0
i X0σ
j +X2σ̄
i X σ̄2
j
)
, (2.3)
H ′
1 =
∑
ij,i 6=j
tij
(
X σ̄0
i Xσ2
j −Xσ0
i X σ̄2
j + h.c.
)
, (2.4)
where µ is the chemical potential, U is the intra-atomic Coulomb repulsion, t ij is the
nearest-neighbour hopping integral, X k
i is the operator of the number of |k〉-states
on i-site; σ denotes the spin of an electron (σ =↓, ↑) and σ̄ denotes the projection
of an electron spin opposite to σ; H0 describes a system in the atomic limit, H1
describes electron hoppings between singly occupied sites and empty sites (holes)
(the first sum in H1 – processes forming “h-band”) and electron hoppings between
doubly occupied sites (doublons) and singly occupied sites (the second sum in H1
– processes forming “d-band”). H ′
1 describes “hybridization” between the “h-band”
and “d-band” (the processes of pair creation and annihilation of holes and doublons).
788
Electron correlations in narrow energy bands
The single-particle Green function is written in X kl
i -operators as
〈〈ap↑|a+s↑〉〉 = 〈〈X↓2
p |X2↓
s 〉〉 − 〈〈X0↑
p |X2↓
s 〉〉 − 〈〈X↓2
p |X↑0
s 〉〉+ 〈〈X0↑
p |X↑0
s 〉〉. (2.5)
The functions 〈〈X↓2
p |X2↓
s 〉〉 and 〈〈X0↑
p |X2↓
s 〉〉 satisfy the equations
(E + µ− U)〈〈X↓2
p |X2↓
s 〉〉 =
δps
2π
〈X↓
p +X2
p〉+ 〈〈
[
X↓2
p , H1
]
−
|X2↓
s 〉〉
+ 〈〈
[
X↓2
p , H ′
1
]
−
|X2↓
s 〉〉,
(E + µ)〈〈X0↑
p |X2↓
s 〉〉 = 〈〈
[
X0↑
p , H1
]
−
|X2↓
s 〉〉+ 〈〈
[
X0↑
p , H ′
1
]
−
|X2↓
s 〉〉, (2.6)
with [A,B]− = AB−BA. To obtain the closed system of equations we apply a new
two-pole approximation, proposed in the work [11]. Suppose in equation (2.6) that
[
X0↑
p , H1
]
−
=
∑
j
ǫ(pj)X0↑
j ,
[
X↓2
p , H1
]
−
=
∑
j
ǫ̃(pj)X↓2
j , (2.7)
where ǫ(pj) and ǫ̃(pj) are non-operator expressions which we calculate using the
method of the work [13]. In the considered model, in the particular case of electron
concentration n=1 in a paramagnetic state we have
ǫ(pj) = ǫ̃(pj) = (1− 2d)tpj, (2.8)
with d = 〈X2
p〉 being the concentration of doublons.
Let us take into account the functions 〈〈
[
X↓2
p ,H ′
1
]
−
|X2↓
s 〉〉 and 〈〈
[
X0↑
p ,H ′
1
]
−
|X2↓
s 〉〉
in Hartree-Fock approximation:
〈〈
[
X↓2
p , H ′
1
]
−
|X2↓
s 〉〉 =
= −
∑
i,i 6=p
tip[〈〈(X↓
p +X2
p )X
0↑
i |X2↓
s 〉〉+ 〈〈X02
p X2↑
i |X2↓
s 〉〉 − 〈〈X↓↑
p X0↓
i |X2↓
s 〉〉]
≃ −
∑
i,i 6=p
tip〈X↓
p +X2
p〉〈〈X0↑
i |X2↓
s 〉〉,
〈〈
[
X0↑
p , H ′
1
]
−
|X2↓
s 〉〉 =
= −
∑
i,i 6=p
tip[〈〈(X0
p +X↑
p )X
↓2
i |X2↓
s 〉〉+ 〈〈X02
p X↓0
i |X2↓
s 〉〉 − 〈〈X↓↑
p X↑2
i |X2↓
s 〉〉]
≃ −
∑
i,i 6=p
tip〈X0
p +X↑
p〉〈〈X↓2
i |X2↓
s 〉〉; (2.9)
this way we neglect the processes describing the “inter-band” hoppings of electrons
which are connected with the spin turning over and the “inter-band” hoppings with
the formation or annihilation of two electrons on the same site.
789
L.Didukh, Yu.Skorenkyy
So we obtain the closed system of equations
(E − µ+ U)〈〈X↓2
p |X2↓
s 〉〉 −
∑
i
ǫ̃(pi)〈〈X↓2
i |X2↓
s 〉〉
+ 〈X↓
p +X2
p〉
∑
i,i 6=p
tip〈〈X↓2
i |X2↓
s 〉〉 =
〈X2
p +X↓
p〉
2π
δps,
(E − µ)〈〈X0↑
p |X2↓
s 〉〉 −
∑
i
ǫ(pi)〈〈X0↑
i |X2↓
s 〉〉
+ 〈X0
p +X↑
p〉
∑
i,i 6=p
tip〈〈X↓2
i |X2↓
s 〉〉 = 0. (2.10)
After the Fourier transformation we obtain solutions of the system of equations (2.10)
〈〈X↓2
p |X2↓
s 〉〉k =
〈X2
p +X↓
p〉
2π
(
A1
k
E − Eh(k)
+
B1
k
E − Ed(k)
)
, (2.11)
A1
k
=
1
2
(
1− U − ǫ(k) + ǫ̃(k)
Ed(k)− Eh(k)
)
, B1
k
= 1− A1
k
,
〈〈X0↑
p |X2↓
s 〉〉k =
〈X2
p +X↓
p〉〈X0
p +X↑
p〉
2π
× t(k)
Ed(k)− Eh(k)
(
1
E − Eh(k)
− 1
E −Ed(k)
)
. (2.12)
Here t(k) is the hopping integral in k−representation and
Eh(k) = −µ+
U
2
+
ǫ(k) + ǫ̃(k)
2
− 1
2
√
[U − ǫ(k) + ǫ̃(k)]2 + 〈X0
p +X↑
p〉〈X↓
p +X2
p 〉(t(k))2, (2.13)
Ed(k) = −µ+
U
2
+
ǫ(k) + ǫ̃(k)
2
+
1
2
√
[U − ǫ(k) + ǫ̃(k)]2 + 〈X0
p +X↑
p〉〈X↓
p +X2
p〉(t(k))2 (2.14)
are the energies of electron in lower (“hole”) and upper (“doublon”) subbands,
respectively; ǫ(k) and ǫ̃(k) are the Fourier components of ǫ(pj) and ǫ̃(pj).
An analogous procedure for functions 〈〈X↓2
p |X↑0
s 〉〉 and 〈〈X0↑
p |X↑0
s 〉〉 gives the
following expressions:
〈〈X↓2
p |X↑0
s 〉〉k = 〈〈X0↑
p |X2↓
s 〉〉k,
〈〈X0↑
p |X↑0
s 〉〉k =
〈X0
p +X↑
p 〉
2π
(
A2
k
E − Eh(k)
− B2
k
E − Ed(k)
)
,
A2
k
= B1
k
, B2
k
= A1
k
. (2.15)
Finally, in k-representation single-particle Green function (2.5) we obtain
〈〈ap↑|a+s↑〉〉k =
1
2π
(
Ak
E −Eh(k)
+
Bk
E −Ed(k)
)
,
790
Electron correlations in narrow energy bands
Ak =
1
2
(
1− (C1 − C2)(U − ǫ(k) + ǫ̃(k)) + 4t(k)C1C2
Ed(k)− Eh(k)
)
,
Bk = 1− Ak, (2.16)
where C1 = 〈X0
p +X↑
p〉, C2 = 〈X2
p +X↓
p 〉.
To calculate the single-particle Green function and energy spectrum we substi-
tute the mean values of diagonal X−operators by their mean values:
〈X2
p〉 = d, 〈X0
p〉 = c. (2.17)
In an important case for the investigation of metal-insulator transition n = 1
(when c = d) in a paramagnetic state (〈X ↑
p〉 = 〈X↓
p〉) from the constraint
〈X0
p +X2
p +X↑
p +X↓
p 〉 = 1, (2.18)
we have the following:
〈X↑
p〉 = 〈X↓
p〉 =
1
2
(1− 2d). (2.19)
Finally, single-particle Green function (2.16) has the form
〈〈ap↑|a+s↑〉〉k =
1
2π
(
Ak
E − Eh(k)
+
Bk
E − Ed(k)
)
,
Ak =
1
2
(
1− t(k)
√
U2 + (t(k))2
)
,
Bk = 1− Ak, (2.20)
where single-particle energy spectrum is
Eh(k) = (1− 2d)t(k)− 1
2
√
U2 + (t(k))2,
Ed(k) = (1− 2d)t(k) +
1
2
√
U2 + (t(k))2 (2.21)
(here we took into account that µ = U/2 for n = 1).
Single-particle Green function (2.20) and energy spectrum (2.21) are exact in the
band and atomic limits. It is worthwile to note that unlike the results of two-pole ap-
proximations of Hubbard [7] and Ikeda, Larsen, Mattuck [14], the energy spectrum
(2.21) depends on polar states concentration (thus on temperature). Unlike the ap-
proximations based on the ideology of Roth [15] (in this connection see also [16–21]),
the energy spectrum (2.21) describes a metal-insulator transition. Energy spectrum
which describes a metal-insulator transition was earlier obtained in work [13]. Un-
like the work [13] where all commutators in the equations (2.6) were taken into
account in the generalized mean-field approximation, here we apply this procedure
only to the commutators of electron operators with the “diagonal” part of Hamil-
tonian which describes hoppings within Hubbard subbands. Other processes are
791
L.Didukh, Yu.Skorenkyy
taken into account by means of Hartree-Fock approximation. As a result, expression
(2.21) differs from the respective expressions in work [13] by the presence of the term
√
U2 + t2(k) instead of
√
U2 + 4d2t2(k). This leads to the series of distinctions be-
tween the results of this work and the results of work [13] (d(U/w)–dependence, the
condition of metal-insulator transition, etc); at the same time expression (2.21) de-
pends on polar state concentration similar to the respective expression in work [13].
3. Energy gap and polar states concentration
The energy gap (difference of energies between bottom of the upper and top of
the lower Hubbard bands) is given by
∆E = Ed(−w)− Eh(w) = −2w(1− 2d) +
√
U2 + w2, (3.1)
(where w = z|t| is the halfwidth of the uncorrelated electron band, z is the number
of the nearest neighbours to a site). Expression (3.1) describes the vanishing of the
energy gap in the spectrum of paramagnetic insulator at critical value (U/w) c when
the halfbandwidth w increases (under pressure).
To calculate the polar states concentration we use the function (2.11). At T = 0
and at a rectangular density of states, the concentration of polar states is
d =
1
4
+
U
8w
ln
(
1− 4d
3− 4d
)
(3.2)
if (U/w) 6 (U/w)c and
d =
1
4
+
U
8w
ln
(
√
1 + (U/w)2 + 1
√
1 + (U/w)2 − 1
)
(3.3)
Figure 1. The dependence of doublon
concentration d on U/w at zero tem-
perature.
if (U/w) > (U/w)c. At T = 0 we have
(U/w)c = 1.672.
The dependence d(U/w) given by
equations (3.2)–(3.3) is plotted on fig-
ure 1. One can see that in the point
(U/w)c the slope of d(U/w)-dependence
changes; the concentration of doublons
vanishes at U/w → ∞. Our result for
d(U/w) in the region of MIT is in good
agreement with the result of papers [9,23]
obtained in the limit of infinite dimen-
sions (figure 2). The parameter U is nor-
malized by the averaged band energy in
the absence of correlation ε0 (we have
ε0 = −w/2 when the density of states is
rectangular). In figure 3 the dependencies
792
Electron correlations in narrow energy bands
Figure 2. The comparison of
d(U/w) dependencies: solid line –
our result, dashed line – iterative-
perturbative theory [9,23], circles –
QMC method [23].
Figure 3. The dependencies of doublon
concentration d on U/w at different
temperatures: lower curve corresponds
to kT/w = 0.16, middle curve corre-
sponds to kT/w = 0.08, upper curve
corresponds to kT/w = 0.
Figure 4. The dependencies of dou-
blon concentration d on temperature
at different U/w: values of U/w from
down to up are 2, 1.5, 1, 0.5, 0; solid
lines correspond to our results, dashed
lines correspond to the result of papers
[9,23].
Figure 5. The dependencies of en-
ergy gap width on U/w: “Hubbard-I”
approximation (upper curve), our re-
sult (middle curve), approximation [13]
(lower curve).
793
L.Didukh, Yu.Skorenkyy
of polar states concentration on parameter U/w at different temperatures are pre-
sented. Note the important difference (see figure 4) of the dependence of d on tem-
perature from the result of papers [9,23]: we found that at any temperature, polar
states concentration increases monotonically with the increasing temperature at the
fixed value of U/w when the respective dependence in [9,23] has a minimum.
Figure 6. The dependencies of energy
gap width on temperature at different
U/w: values of U/w from down to up
are 0.5, 1.2, 1.5.
Figure 7. The comparison of ground
state energies in one-dimensional case:
dashed curves correspond to upper and
lower bounds given by Langer and
Mattis [26], upper solid curve corre-
sponds to exact ground state (Lieb and
Wu [25]) lower solid curve corresponds
to the result of this paper.
The dependence of ∆E/U on param-
eter U/w at zero temperature is plotted
in figure 5. It is important to note that
in the point of gap disappearence d 6= 0
by contrast to the previously obtained re-
sult [13]. At the increasing U/w, the en-
ergy gap width increases (the negative
values of ∆E correspond to the overlap-
ping of the subbands). For comparison
in figure 5 the results of approximation
“Hubbard-I” [7] are also plotted. In the
point of energy gap vanishing (U/w)c =
1.672 which is very close to the result of
“Hubbard-III” approximation [22].
At the increase of temperature in
the metallic state, the overlapping of
subbands decreases and temperature in-
duced transition from metallic to insu-
lating state can occur at some values of
parameter U/w (figure 6). The depen-
dence obtained can qualitatively explain
the transitions from metallic to insulating
state with the increase of temperature in
the systems NiS2−xSex, (V1−xCrx)2O3 and
Y1−xCaxTiO3) experimentally observed
in a paramagnetic state. Note that the
quantitative description of the pressure-
temperature phase diagram of these com-
pounds within the generalized Hubbard
model with correlated hopping has been
done in [24].
4. Ground state energy
The ground state energy of the model
E0
N
=
1
N
〈
∑
ijσ
tija
+
iσajσ〉+ Ud, (4.1)
794
Electron correlations in narrow energy bands
Figure 8. The ground state energy
found in this paper (upper curve), best
upper (middle curve) and lower (lower
curve) bounds on ground state energy
in infinite-dimensional case.
Figure 9. The upper (upper curve) and
lower (lower curve) bounds on ground
state energy in three-dimensional
case [26] and the ground state energy
found in this paper (middle curve).
calculated using single particle Green function (2.20) and expressions (3.2)–(3.3) for
the concentration of polar states has the form:
E0
N
= −w
2
+
U
4
(1 + 3d)− U2
2w
(1− 4d)
4(1− 2d)2 − 1
(4.2)
if (U/w) 6 (U/w)c and
Figure 10. The kinetic part of ground
state energy as a function of U/w.
E0
N
= −1
2
√
U2 + w2 + 2U(
1
4
− d) (4.3)
if (U/w) > (U/w)c. In figure 7 the depen-
dence of the ground state energy on the
parameter U/w given by equations (4.2)–
(4.3) is compared with the exact result
found in one-dimensional case [25]. The
upper and lower bounds on ground state
energy in one-dimensional case found in
paper [26] are also shown. Our result for
the ground state energy in a metallic state
lies slightly lower than the exact one and
in the insulator state it very well fits the
exact ground state energy.
In figure 8 our plot of the ground state
energy is compared with the best upper
and lower bounds on ground state energy
795
L.Didukh, Yu.Skorenkyy
in infinite-dimensional case [27]. In figure 9 we have the comparison with bounds on
ground state energy for three-dimensional simple cubic lattice obtained in paper [26].
In Figs. 7–9 the ground state energy per electron is normalized by the averaged band
energy in the absence of correlation ε0; in the considered case and rectangular density
of states ε0 = −w/2. Figs. 7–9 show that our result present a good approximation
for the ground state energy of the system. In figure 10 we plot our result for the
kinetic part of ground state energy. This plot describes the same behavior of kinetic
energy of electrons with the change of correlation strength in a paramagnetic state
like the respective result of work [23]: in a metallic state the absolute value of kinetic
energy decreases rapidly due to a rapid decrease of doublon (hole) concentration. In
the insulating state the absolute value of kinetic energy decreases slowly which in
the approximation of the effective Hamiltonian (obtained for the case t ij/U ≪ 1) is
equivalent to the interaction of local magnetic moments.
5. Conclusions
In this paper we have studied electron correlations in narrow energy bands using
the recently proposed approximation [11]. We assume that the state of the narrow-
band system is a paramagnetic insulator or a paramagnetic metal. The single-particle
Green function and the energy spectrum dependent on model parameters and on
polar states concentration (thus on temperature) have been found in a paramagnetic
state at half-filling (n = 1). The obtained expression for energy gap permits to de-
scribe MIT at the changes of bandwidth (pressure) or temperature. The comparison
of the calculated ground state energy with the results of other approximations and
the exact result found in one-dimensional case shows that the method used is a good
approximation for the model under consideration.
It is worthwhile noting that the approximation used in this paper can be gen-
eralized to describe the effects of antiferromagnetic ordering. Such a generalization
will be considered in the subsequent paper.
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Електроннi кореляцiї у вузьких енергетичних зонах:
енергiя основного стану та перехiд
метал-дiелектрик
Л.Дiдух, Ю.Скоренький
Тернопiльський державний технiчний унiверситет iменi I. Пулюя,
кафедpа фiзики, 46001 Тернопiль, вул. Руська, 56
Отримано 5 травня 2000 р., в остаточному вигляді –
28 жовтня 2000 р.
В данiй роботi електроннi кореляцiї у вузьких енергетичних зонах
вивчаються в рамках моделi Габбарда. За допомогою нового дво-
полюсного наближення знайдено одночастинкову функцiю Грiна та
енергетичний спектр у парамагнiтному станi при половинному за-
повненнi. В основному станi знайдено аналiтичнi вирази для шири-
ни енергетичної щiлини, концентрацiї полярних станiв та енергiї си-
стеми. Дослiджено переходи метал-дiелектрик при змiнi ширини зо-
ни та при змiнi температури. Отриманi результати використанi для iн-
терпретацiї деяких експериментальних даних для вузькозонних ма-
терiалiв.
Ключові слова: вузькi зони провiдностi, гамiльтонiан Габбарда,
перехiд метал-дiелектрик, енергiя основного стану
PACS: 71.28.+d, 71.27.+a, 71.10.Fd, 71.30.+h
798
|
| id | nasplib_isofts_kiev_ua-123456789-120984 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-01T04:37:29Z |
| publishDate | 2000 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Didukh, L. Skorenkyy, Yu. 2017-06-13T12:07:03Z 2017-06-13T12:07:03Z 2000 Electron correlations in narrow energy bands: ground state energy and metal-insulator transition / L. Didukh, Yu. Skorenkyy // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 787-798. — Бібліогр.: 27 назв. — англ. 1607-324X DOI:10.5488/CMP.3.4.787 PACS: 71.28.+d, 71.27.+a, 71.10.Fd, 71.30.+h https://nasplib.isofts.kiev.ua/handle/123456789/120984 The electron correlations in narrow energy bands are examined within the framework of the Hubbard model. The single-particle Green function and energy spectrum are obtained in a paramagnetic state at half-filling by means of a new two-pole approximation. Analytical expressions for the energy gap, polar states concentration and energy of the system are found in the ground state. Metal-insulator transitions in the model at the change of bandwidth or temperature are investigated. The results obtained are used for interpretation of some experimental data in narrow-band materials. В данiй роботi електроннi кореляцiї у вузьких енергетичних зонах вивчаються в рамках моделi Габбарда. За допомогою нового двополюсного наближення знайдено одночастинкову функцiю Грiна та енергетичний спектр у парамагнiтному станi при половинному заповненнi. В основному станi знайдено аналiтичнi вирази для ширини енергетичної щiлини, концентрацiї полярних станiв та енергiї системи. Дослiджено переходи метал-дiелектрик при змiнi ширини зони та при змiнi температури. Отриманi результати використанi для iнтерпретацiї деяких експериментальних даних для вузькозонних матерiалiв. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Electron correlations in narrow energy bands: ground state energy and metal-insulator transition Електроннi кореляцiї у вузьких енергетичних зонах: енергiя основного стану та перехiд метал-дiелектрик Article published earlier |
| spellingShingle | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition Didukh, L. Skorenkyy, Yu. |
| title | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition |
| title_alt | Електроннi кореляцiї у вузьких енергетичних зонах: енергiя основного стану та перехiд метал-дiелектрик |
| title_full | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition |
| title_fullStr | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition |
| title_full_unstemmed | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition |
| title_short | Electron correlations in narrow energy bands: ground state energy and metal-insulator transition |
| title_sort | electron correlations in narrow energy bands: ground state energy and metal-insulator transition |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/120984 |
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