Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain
We study the AB2 "dimmer-connector" chain within a generalized Hubbard model, which contains site-dependent parameters, and different chemical potentials for A and B sites. Considering one electron per atom, we carry out exact calculations for finite clusters, and derive some asymptotic re...
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| Опубліковано в: : | Condensed Matter Physics |
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Інститут фізики конденсованих систем НАН України
2010
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| Цитувати: | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain / J. Rössler, D. Mainemer // Condensed Matter Physics. — 2010. — Т. 13, № 1. — С. 13704: 1-8. — Бібліогр.: 15 назв. — англ. |
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| author | Rössler, J. Mainemer, D. |
| author_facet | Rössler, J. Mainemer, D. |
| citation_txt | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain / J. Rössler, D. Mainemer // Condensed Matter Physics. — 2010. — Т. 13, № 1. — С. 13704: 1-8. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | We study the AB2 "dimmer-connector" chain within a generalized Hubbard model, which contains site-dependent parameters, and different chemical potentials for A and B sites. Considering one electron per atom, we carry out exact calculations for finite clusters, and derive some asymptotic results, valid for macroscopic chains. We take a non-vanishing intra-dimmer electron hopping, thus departing from the condition of a bipartite lattice. In spite of that, the system persists ferrimagnetic in some region of the parameter space, thus generalizing a theorem of Lieb for bipartite lattices. A somewhat surprising result is that the ferrimagnetic phase is possible, even for a very large chemical potential jump between A and B sites. In another respect, we show that a previously reported macroscopic (2N) degenerancy of the AB2 Heisenberg chain ground state (GS) is fully removed on going to the (more fundamental) Hubbard model, yielding a non-magnetic GS.
|
| first_indexed | 2025-12-07T17:19:11Z |
| format | Article |
| fulltext |
Condensed Matter Physics 2010, Vol. 13, No 1, 13704: 1–8
http://www.icmp.lviv.ua/journal
Ferrimagnetism in the Hubbard, dimmer-connector
frustrated chain
J. Rössler∗, D. Mainemer
Departamento de Fı́sica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
Received April 21, 2009, in final form February 24, 2010
We study the AB2 “dimmer-connector” chain within a generalized Hubbard model, which contains site-
dependent parameters, and different chemical potentials for A and B sites. Considering one electron per
atom, we carry out exact calculations for finite clusters, and derive some asymptotic results, valid for macro-
scopic chains. We take a non-vanishing intra-dimmer electron hopping, thus departing from the condition of
a bipartite lattice. In spite of that, the system persists ferrimagnetic in some region of the parameter space,
thus generalizing a theorem of Lieb for bipartite lattices. A somewhat surprising result is that the ferrimagnetic
phase is possible, even for a very large chemical potential jump between A and B sites. In another respect,
we show that a previously reported macroscopic (2N ) degenerancy of the AB2 Heisenberg chain ground
state (GS) is fully removed on going to the (more fundamental) Hubbard model, yielding a non-magnetic GS.
Key words: Hubbard model, Heisenberg model, ferrimagnetic order, frustration, lozenge lattice, dimmer
PACS: 73.90.+f, 75.10.Lp, 75.10–75.25
1. Introduction
Although the Hubbard model was introduced in order to explain itinerant ferromagnetism
(FM), the appearance of a truly ferromagnetic phase has been somewhat elusive. Nagaoka [1]
obtained FM in a very punctual case (U → ∞ limit and a single hole in a half-filled band). Long
range electron hopping may also yield ferromagnetism, even in one dimension [2, 3]; the latter
results may be associated with the frustrating effect introduced by the different hoppings.
An important theorem due to E. Lieb [4] establishes the existence of FM in a more ample
context, this is the case of a half-filled band system, with the topology of a bipartite lattice
Λ = A + B. Under such hypothesis, the net spin of the ground state becomes S = 1
2
| |A| − |B| |;
here |A|, |B| denote the number of sites in each sublattice. Therefore, a net (macroscopic) magnetic
moment exists when the number of sites in the two sublattices differ, |A| 6= |B|. The lattice
topology is defined by the non-vanishing hopping amplitudes, and in this bipartite case a non-
vanishing hopping ta,b 6= 0 only occurs when a ∈ A and b ∈ B or vice versa; otherwise ta,b = 0.
This “two sublattice ferrimagnetism” of Lieb can be easily understood in the strongly interacting
(U → ∞) limit, where a half-filled band Hubbard model becomes equivalent to a Heisenberg
Hamiltonian with positive exchanges [5]. Accordingly, an antiferromagnetic (AF) coupling exists
between the sites of A and B sublattices linked by non-vanishing hopping amplitudes, while no
coupling exists between the spins lying in the same sublattice. In this way, the spins of the B
sublattice surrounding a given spin of the A sublattice are antiparallel to such a spin, and therefore,
they dispose parallel to each other. Extending this argument to the whole lattice we conclude that
each sublattice has an internal ferromagnetic order, while the magnetic moment of the A and B sub-
lattices disposes antiparallel one another, thus yielding a ferrimagnetic (instead of ferromagnetic)
order. This argument can be applied even to one-dimensional topologies; that is the case of the
“lozenge lattice” for example [6–8], where the Hubbard GS is ferrimagnetic in the half-filled band
case.
∗E-mail: jrossler.fisica@gmail.com
c© J. Rössler, D. Mainemer 13704-1
http://www.icmp.lviv.ua/journal
J. Rössler, D. Mainemer
We illustrate former concepts by means of the “connector-dimmer” AB2 chain (see figure 1);
there the B sublattice corresponds to the dimmers, while the A sublattice contains the “connec-
tors” of reference [9]. This chain transforms into the bipartite “lozenge” lattice when the hopping
amplitude between the B sites on the same dimmer vanishes (vertical lines in figure 1). In this
case, Lieb’s theorem [4] ensures that the net spin of the chain is S = 1
2
N , where N is the number
of lattice cells.
Figure 1. The AB2 “dimmer-connector” chain. The full circles are the connectors, while vertical
“dumbbells” are the B2 dimmers.
The AB2 chain has been studied in the context of Heisenberg [9–11] and half-filled band Hub-
bard [6–8] models. While [9–11] include two antiferromagnetic exchanges, J (connecting A-B sites)
and J0 (connecting both B sites on the same dimmer), [6–8] only consider a non-vanishing elec-
tronic hopping between A and B sites (say, a “lozenge” Hubbard lattice), in order to satisfy Lieb’s
hypothesis of a bipartite lattice [4]. Lieb’s results were generalized, showing that the ferrimagnetic
order persists in the “lozenge” and in other one-dimensional lattices, when site dependent Hubbard
parameters are considered [7].
On taking the Heisenberg (U → ∞) limit, the lozenge Hubbard chain transforms into an al-
ternate arrangement of s = 1
2
(connector sites) and s = 1 (dimmer sites) spins with AF coupling
J > 0 (while the intra-dimmer coupling vanishes, J0 = 0). In spite of the effect of quantum fluc-
tuations (which are especially relevant in one-dimension), this one-dimensional lattice yields a long
range ferrimagnetic order [12], with a total spin per cell S = 1
2
.
2. The model
The aim of this contribution is to establish whether the Lieb’s FM ground state (GS) persists, if
we depart from the bipartite lattice hypothesis by introducing a non-vanishing hopping t0 between
the two B sites on the same dimmer (see figure 1). Several actual systems may be described by
such kind of lattices [13].
We shall describe the AB2 chain using a generalized Hubbard model, with the associated
Hamiltonian
HU = −
∑
`,σ
[
t
(
a†
`,σ + a†
`+1,σ
)
(b`,1,σ + b`,2,σ) + t0 b†`,1,σ b`,2,σ + Hermit. Conj.
]
+
∑
`,σ
[
EA a†
`,σa`,σ +
UA
2
a†
`,σ a`,σa†
`,−σ a`,−σ
]
+
1
2
UB
∑
`,σ
[
b†`,1,σ b`,1,σb†`,1,−σ b`,1,−σ + b†`,2,σ b`,2,σb†`,2,−σ b`,2,−σ
]
(1)
here a†
`,σ and b†`,j,σ create a spin σ electron on sites A and Bj (j = 1, 2) respectively, in the `-th
cell (see figure 1). UA and UB are the corresponding Coulomb repulsions, while EA measures the
chemical potential on a site A, taking EB = 0 as reference. Equation (1) is a generalization of
the Hamiltonian considered in reference [7], since we introduce an intra-dimmer hopping t0 and
different chemical potentials for nonequivalent sites, following a quite natural physical requisite.
13704-2
Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain
This Hamiltonian has several “global” symmetries, such as the (obvious) translational, inver-
sion and spin rotation invariances (see also [7]). Furthermore, HU has a “local inversion symme-
try” associated with each dimmer `. Such a symmetry implies the conservation of the total spin
~S2
u,` = Su,` (Su,` + 1) of the “antibonding” state u†
`,σ = (b†`,1,σ − b†`,2,σ)/
√
2 on dimmer `. The
components of ~Su,` are
Sx + iSy = u†
`,↑u`,↓ and Sz =
1
2
(u†
`,↑ u`,↑ − u†
`,↓ u`,↓).
This conservation law implies:
(i) For some sites `, it holds that Su,` = 1/2 and
∑
σ u†
`,σ u`,σ = 1. Therefore, those sites always
contain an unpaired antibonding electron u†
`,σ, although its spin σ may fluctuate.
(ii) Otherwise Su,` = 0, and then
∑
σ u†
`,σ u`,σ = { 0, 2 }. In those sites the antibonding states
are created or annihilated in pairs, u†
`,↑u
†
`,↓.
These “local” constants of motion (existing for each ` dimmer), simplify (to some extent) the
many-body problem associated with Hamiltonian (1).
On applying an electron-hole transformation, the Hamiltonian HU preserves its general form
(excepting for an irrelevant additive constant), but the parameters t0, EA and EB modify as follows:
t0 → −t0 and EA − EB → EB − EA + UB − UA (remember that we chose EB = 0). The sign
of t is irrelevant, since we can change it by introducing a phase factor −1 on the operators a†
`,σ. In
contrast, the sign of t0 is quite relevant, since the lattice has “electronic kinetic frustration” [14]
due to the dimmer-connector triangles.
3. Strong interaction limit
We first consider the limit case |t0| � UB and |t| � UA + EA, UB − EA. The latter inequality
presupposes 0 < UA + EA, UB −EA, thus ensuring that a neutral configuration (each site accom-
modating one electron) is the system GS in the limit |t|, |t0| → 0. Using a Schrieffer-Wolff transfor-
mation, and projecting over the “neutral” Hilbert subspace (where double occupied or empty sites
are excluded, hence each site has attached a spin one-half operator), the Hubbard Hamiltonian HU
transforms into a Heisenberg Hamiltonian HH [5]. Generalizing such transformation to the present
model, we conclude
HH = J
∑
`,σ
~SA,` ·
(
~F`−1 + ~F`
)
+ J0
∑
`,σ
~SB1, ` · ~SB2, ` , (2)
where ~F` = ~SB1, ` + ~SB2, ` is the total spin of dimmer `. Here the individual, one-half spins
~SA,` and ~SBj,` are attached to A and Bj sites, respectively (j = 1, 2). The exchange energies J0
(intra-dimmer) and J (connector-dimmer) are
J0 =
4 t20
UB
and J = 2 t2 ( gA + gB)
with gA =
1
UA + EA
and gB =
1
UB − EA
, (3)
respectively. We note that ~F 2
` = F`(F` + 1) is a constant of motion for each `.
The spin Hamiltonian HH was studied by Niggemann et al. [10], and other authors [9–11].
Introducing the ratio
R ≡ J
J0
=
UBt2
2t20
( gA + gB ) , (4)
we summarize their conclusions for the GS:
13704-3
J. Rössler, D. Mainemer
(i) When R > 1.10 (small t0 case), it holds that F` = 1 ∀`. Here the system is in the Kolezhuk
“Ferrimagnetic Phase” [12] (labeled as P∞ in the literature [9]), where spins 1 (dimmers)
and 1/2 (connectors) alternate, and the antiferromagnetic coupling yields a non-zero global
spin S = N/2 (in spite of quantum fluctuations).
(ii) For 0.5 < R < 1.10, it holds that F2` = 1, F2`−1 = 0, and the system is in the phase of a
period two (labeled as P2 in the literature [9]). However, the antiferromagnetic exchange J
couples the (non-zero) dimmer spin F2` to its neighbors, SA, 2` and SA, 2`+1, thus yielding a
singlet (non-magnetic) state.
(iii) Finally, for R < 0.5 (large t0 case), the GS corresponds to the state with F` = 0 for all `
(the so-called P1 phase [9]). Here the GS has a degenerancy 2N , where N is the number of
cells. This macroscopic degenerancy is due to the fact that the energy does not depend on
the orientation of each “connector” spin ~SA,`.
However, this degenerancy is removed on going to the (more fundamental) Hubbard model. In
fact, on considering the limit case |t| � |t0| � UA, UB and applying the fourth order perturbation
theory (instead of the second order analysis that leads to equation (2)), we conclude that the low
lying energy states can be described by an effective Heisenberg Hamiltonian
Heff =
∑
`
Jcc
~SA,` · ~SA,`+1 (5)
with a residual connector-connector coupling Jcc > 0 given by
Jcc = 4 t4
[
1
UA
(gA − gB)
2
+ gA g2
B + g2
A gB + 2 g3
A + 2 g3
B
]
. (6)
This way, the GS becomes non-degenerate, showing the existence of antiferromagnetic short
range correlations between the connector spins.
4. Small cluster calculations
In order to depart from the UA, UB → ∞ limit, we analyze the Hamiltonian (1) for a 5-atom
(butterfly-like) cluster, consisting of a connector and two neighboring dimmers. In addition, we also
consider a 9-atom (3 dimmers, 3 connectors) ring in order to study the particular limit EA → −∞.
Although such small clusters cannot reproduce the thermodynamic (N → ∞) limit, at least they
may retain the main physical features of the larger ones. On the other hand, it is easy to obtain
the symmetry properties and conserved magnitudes of these small clusters. We mainly focus on
the half filling case. We restrict ourselves to the zero temperature case (GS properties), since the
phase diagram becomes blurred for a finite cluster at non-zero temperature.
In the case of the butterfly-like cluster with 5 electrons, the associated Hilbert space has a
dimension 252, but using group theory techniques the Hamiltonian can be broken into 18 × 18 or
smaller blocks. In fact, on considering the cluster symmetries (including the “local” inversion at
each dimmer), the Hamiltonian group is isomorphic to D2, d ⊗ SU2 (here we use the nomenclature
by Hamermesh [15]); SU2 describes the spin rotational symmetry, classified by the total spin
quantum number S =
{
1
2
, 3
2
, 5
2
}
.
Depending on the parameters of the system, the GS can be on the irreducible representations
(IR) [B1, S = 3/2], [E, S = 1/2] and [A1, S = 1/2]. The B1 states are odd to local inversion in
both dimmers, the A1 states are even in both dimmers, while the E states are odd with respect to
one dimmer and even with respect to the other one. The associated values of “antibonding spin”
are Su,` = 1/2 at an odd dimmer, and Su,` = 0 at an even dimmer.
We first consider the Heisenberg UA, UB → ∞ limit for our “butterfly cluster”. Here we can
identify the IR [B1, S = 3/2] GS as the ferrimagnetic ( P∞ ) phase, since this IR corresponds to
F1 = 1 = F2 , ~F1 · ~F2 = +1 and (~F1 + ~F2) · ~SA = −3 / 2 , thus showing the typical ferrimag-
netic correlations (the dimmer spins are parallel to each other, and antiparallel to the connector
spin).
13704-4
Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain
In the case where the GS belongs to the IR [E, S = 1/2] , it holds that F1 = 1 , F2 = 0 and
~F1 · ~SA = −1 . Accordingly, this IR corresponds to the P2 phase previously described.
Finally, if the GS belongs to the IR [A1, S = 1/2] , both dimmer spins vanish F1 = 0 = F2 .
Therefore we identify the IR [A1, S = 1/2] as the P1 phase.
Due to the finite size and shape of the cluster, the phase diagram in the Heisenberg UA, UB → ∞
limit does not correspond to the N = ∞ case described below equation (4). Now the GS be-
longs to the IR [B1, S = 3/2] ( P∞ phase) for R > 2, while the IRs [E, S = 1/2] ( P2 phase) and
[A1, S = 1/2] ( P1 phase) are stable for 1 < R < 2 and R < 1 respectively.
We carry out calculations of spin-spin correlations for the GS of the Hubbard model (with
finite values of UA, UB) at the different phases displayed by the system, concluding the results
qualitatively similar to those of the Heisenberg model. Accordingly, we can use the former associ-
ation between the IRs of the GS and the Pj phases, j = {1, 2,∞}. In this way, when the GS has
S = 3/2, the system is in the ferrimagnetic P∞ phase, while a GS with S = 1/2 corresponds
to a non-magnetic phase (remember that the number of electrons (5) is odd, thus excluding the
S = 0 case).
(a) (b)
(c) (d)
Figure 2. The phase diagram of the “butterfly cluster” for different parameters of the generalized
Hubbard model. The ferrimagnetic region is shown as the shaded area. (a) An UB versus t0 plot,
with UA = 5, EA = 0, and t = 1. Here the Heisenberg ferrimagnetic boundary (solid line) is
also shown for comparison. A logarithmic scale is used for UB . (b) An EA versus t0 plot, with
UA = 5, UB = 3, and t = 1. (c) A t versus t0 plot, with UA = 0, UB = 1, and EA = 2. (d)
An UB versus t0 plot, with UA = 0, EA = 0, and t = 1.
13704-5
J. Rössler, D. Mainemer
The numerical analysis of the “butterfly” Hubbard cluster is summarized in figures 2 (a–d).
The shaded area represents the stability region of the ferrimagnetic phase. The main conclusions
of our study are:
(a) The description of the system by the Heisenberg Hamiltonian is not suitable, excepting for
extremely large values of the Coulomb repulsions UA, UB, departing very fast from it as
more realistic values are considered. For example, on taking |t| / UA , |t0| / UB ∼ 0.15, the
magnetic-nonmagnetic boundary becomes J / J0 ∼ 5 (instead of the Heisenberg prediction,
J / J0 = 2). In this way, the “Heisenberg limit” description largely overestimates the size of
the magnetic region for small and intermediate values of Coulomb repulsion UB , erroneously
predicting too large values for |t0| at the ferrimagnetic-nonmagnetic boundary. However,
for larger values of UB and t0 < 0 the Heisenberg description underestimates the size of
the ferrimagnetic zone. We compare the Hubbard and Heisenberg magnetic boundaries in
figure 2 (a).
(b) While the generalized Lieb’s theorem [7] only ensures a ferrimagnetic GS under the hypothesis
t0 → 0 , UA, UB > 0 and EA = 0, our numerical calculations yield ferrimagnetism well
beyond the scope of that theorem, as we shall detail in what follows.
(c) The sign of t0 becomes relevant (see figures 2 (a, b)), especially for large values of |UA − UB |.
This is due to the “electronic kinetic frustration” [14] and the absence of electron-hole inver-
sion symmetry (only present when EA = (UB − UA)/2).
According to figure 2 (b) the case t0 < 0 favors magnetism for EA < 0 (say, when the
connector corresponds to an anion), while the converse is true for EA > 0. This is confirmed
by the asymptotic relations for the magnetic boundaries:
−
√
UBt2/2 |EA| < t0 < 5 t2/4 |EA| (case EA → −∞)
and
−5 t2/4 EA < t0 <
√
UB t2/2EA (case EA → +∞ ).
(d) The latter asymptotic relations imply that a ferrimagnetic region is still present in the
|EA| → ∞ limit, in accordance with figure 2 (b). This is a somewhat surprising behav-
ior, since the charge in the connector is fixed in that limit (the existing zero electrons for
EA → +∞, and two for EA → −∞) and therefore the two dimmers are expected to be di-
sconnected due to the blocking of electron hopping through the connector (as long as charge
fluctuations are absent in the connector site).
This behavior seems to be associated with the electron number. In fact, working with 4
(instead of 5) electrons in our “butterfly” cluster, the ferrimagnetic phase disappears for large
enough |EA|. We have also considered a 3-dimmer-3-connector ring with 9 electrons (say, one
electron per atom) in the EA → −∞ limit (which may be important in actual systems with
very electronegative bridges connecting magnetic groups). In this case a magnetic region is
present for t0 < 0, although it is restricted to a very narrow region of the phase space. At
present we are analyzing this point by considering larger clusters and different number of
electrons.
(e) A ferrimagnetic GS is also present in the case of zero Hubbard repulsion in the connector
site, UA = 0 , as it can be inferred from figures 2 (c, d). Indeed, we have checked that the
magnetic-non-magnetic boundary is nearly independent of the UA value.
(f) However, a non-vanishing UB is essential for the appearance of magnetism, since the fer-
rimagnetic region shrinks to zero as UB → 0 (see figures 2 (a, d)). The magnetic region
increases with UB , showing the existence of a linear relation for small values of UB. In parti-
cular, for a large inter-dimmer kinetic energy t, the magnetic region is approximately given
by the condition |t0| < 0.22 UB � t.
13704-6
Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain
(g) We can summarize the complete phase diagram as follows: There is a narrow ferrimagnetic
region (existing for small values of |t0|), identified with the IR [B2, S = 3 / 2], and associated
with the P∞ phase of the dimmer-connector Heisenberg chain [9–11]. Here the “antibonding”
states are single occupied in each dimmer, Su,1 = Su,2 = 1/2 .
For intermediate values of |t0| the GS lies in the IR [E, S = 1 / 2] (associated with the P2
phase of the Heisenberg limit). This region is very broad, in comparison to the ferrimagnetic
one. Here Su,1 = 1/2 and Su,2 = 0 in our finite cluster calculations.
Finally, for larger values of |t0| the IR [A1, S = 1 / 2] (associated with the P1 phase [9]) be-
comes the GS; here Su,1 = 0 = Su,2 . The boundary between the [E, S = 1 / 2] and [A1, S =
1/2] regions is crudely described by the Heisenberg limit condition R ∼ 1 , see equation (4).
5. Summary
We have studied the AB2 “dimmer-connector” chain within a generalized Hubbard model,
which contains site-dependent parameters. The half filled band case was considered. Our main
objective was to determine whether a ferrimagnetic GS persists as we depart from Lieb’s theorem
hypothesis [4],[7] of a bipartite lattice. For that purpose we introduced a non-vanishing intra-dimmer
hopping t0. We also included a finite jump in the chemical potential, EA, on going from B to A
sublattice.
We established that the present system has a “local” symmetry at each dimmer, which implies
the creation or annihilation of the “antibonding” states in pairs. Therefore the “antibonding” spin,
Su,` =
{
0, 1
2
}
, is conserved.
We first analyzed the small hopping energies, |t|, |t0| → 0 and strong Hubbard repulsions limit.
In this case the system can be described by a Heisenberg Hamiltonian. We concluded that the
GS is ferrimagnetic for (t0 / t)2 < 0.45 UB(gA + gB) (see definitions at equation (3)); otherwise
the system is non-magnetic. We also showed that a previously reported [9] macroscopic (2N )
degenerancy on the Heisenberg “dimmer-connector” chain is fully removed on going to the Hubbard
description.
For finite values of Hubbard repulsions, we carried out small cluster (exact) calculations. We
scanned the parameter space, concluding that there always exists a finite interval t0,1 < t0 < t0,2
where the GS is ferrimagnetic. In contrast with the Heisenberg limit, here |t0,1| 6= t0,2. In fact,
a negative t0 enhances ferrimagnetism if UB → +∞ or EA → −∞ , while a positive t0 favors
ferrimagnetism in the limit EA → +∞ (see figures 2 (a, b)). Indeed, the sign of t0 becomes
relevant when third order processes in the kinetic energy are considered, and the “electronic kinetic
frustration” [14] manifests.
Though a non-vanishing Hubbard repulsion at dimmer sites (UB 6= 0) is an essential requisite
for ferrimagnetism, this phase may persist even in the absence of Coulomb repulsion at connector
sites, UA = 0 .
A somewhat surprising conclusion is the persistence of ferrimagnetism, even in the limit EA →
±∞. However, this result is sensitive to the particular electron occupancy.
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Феримагнетизм у димер-конекторному фрустрованому
ланцюжку Габбарда
Дж. Рьослер, Д. Майнемер
Вiддiл фiзики, факультет природничих наук, Унiверситет Чилi, Касiлла 653, Сантьяго, Чилi
Ми дослiджуємо узагальнену модель Габбарда на АВ2 “димер-конекторному” ланцюжку, яка мiстить
вузловозалежнi параметри i рiзнi хiмiчнi потенцiали для вузлiв А i В. Розглядаючи випадок одно-
го електрона на вузол, ми виконуємо точнi обчислення для скiнчених кластерiв i отримуємо деякi
асимптотичнi результати, справедливi для макроскопiчних ланцюжкiв. Ми припускаємо незникаю-
чий iнтрадимерний електронний перенос, вiдходячи таким чином вiд випадку подвiйної ґратки (дво-
пiдґраткового випадку). Незважаючи на це, система залишається феримагнiтною у деякiй областi
простору параметрiв, що є узагальненням теореми Лiба для подвiйних ґраток. Дещо несподiваним
є результат, що феримагнiтна фаза можлива навiть для дуже великого стрибка хiмiчного потенцiа-
лу мiж вузлами А i В. З iншого боку, ми показуємо, що ранiше вказане макроскопiчне (2N -кратне)
виродження основного стану АВ2 ланцюжка Гайзенберга цiлком знiмається при переходi до (бiльш
фундаментальної) моделi Габбарда, приводячи до немагнiтного основного стану.
Ключовi слова: модель Габбарда, модель Гайзенберга, феримагнiтний порядок, фрустрацiї,
ромбiчна ґратка, димер
13704-8
Introduction
The model
Strong interaction limit
Small cluster calculations
Summary
|
| id | nasplib_isofts_kiev_ua-123456789-32048 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T17:19:11Z |
| publishDate | 2010 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Rössler, J. Mainemer, D. 2012-04-06T18:01:58Z 2012-04-06T18:01:58Z 2010 Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain / J. Rössler, D. Mainemer // Condensed Matter Physics. — 2010. — Т. 13, № 1. — С. 13704: 1-8. — Бібліогр.: 15 назв. — англ. 1607-324X PACS: 73.90.+f, 75.10.Lp, 75.10--75.25 https://nasplib.isofts.kiev.ua/handle/123456789/32048 We study the AB2 "dimmer-connector" chain within a generalized Hubbard model, which contains site-dependent parameters, and different chemical potentials for A and B sites. Considering one electron per atom, we carry out exact calculations for finite clusters, and derive some asymptotic results, valid for macroscopic chains. We take a non-vanishing intra-dimmer electron hopping, thus departing from the condition of a bipartite lattice. In spite of that, the system persists ferrimagnetic in some region of the parameter space, thus generalizing a theorem of Lieb for bipartite lattices. A somewhat surprising result is that the ferrimagnetic phase is possible, even for a very large chemical potential jump between A and B sites. In another respect, we show that a previously reported macroscopic (2N) degenerancy of the AB2 Heisenberg chain ground state (GS) is fully removed on going to the (more fundamental) Hubbard model, yielding a non-magnetic GS. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain Феримагнетизм у димер-конекторному фрустрованому ланцюжку Габбарда Article published earlier |
| spellingShingle | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain Rössler, J. Mainemer, D. |
| title | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain |
| title_alt | Феримагнетизм у димер-конекторному фрустрованому ланцюжку Габбарда |
| title_full | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain |
| title_fullStr | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain |
| title_full_unstemmed | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain |
| title_short | Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain |
| title_sort | ferrimagnetism in the hubbard, dimmer-connector frustrated chain |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/32048 |
| work_keys_str_mv | AT rosslerj ferrimagnetisminthehubbarddimmerconnectorfrustratedchain AT mainemerd ferrimagnetisminthehubbarddimmerconnectorfrustratedchain AT rosslerj ferimagnetizmudimerkonektornomufrustrovanomulancûžkugabbarda AT mainemerd ferimagnetizmudimerkonektornomufrustrovanomulancûžkugabbarda |