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research
Frustrated spin-
1
2
\frac{1}{2}
2
1
Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the
J
1
J_{1}
J
1
--
J
2
J_{2}
J
2
--
J
1
⊥
J_{1}^{\perp}
J
1
⊥
model
Authors
R. F. Bishop
O. Götze
P. H. Y. Li
J. Richter
Publication date
1 January 2019
Publisher
'American Physical Society (APS)'
Doi
Cite
View
on
arXiv
Abstract
The zero-temperature phase diagram of the spin-
1
2
\frac{1}{2}
2
1
J
1
J_{1}
J
1
--
J
2
J_{2}
J
2
--
J
1
⊥
J_{1}^{\perp}
J
1
⊥
model on an
A
A
AA
AA
-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths
J
1
>
0
J_{1}>0
J
1
>
0
and
J
2
≡
κ
J
1
>
0
J_{2} \equiv \kappa J_{1}>0
J
2
≡
κ
J
1
>
0
, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength
J
1
⊥
≡
δ
J
1
J_{1}^{\perp} \equiv \delta J_{1}
J
1
⊥
≡
δ
J
1
. The magnetic order parameter
M
M
M
(viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the N\'{e}el or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when
δ
0
\delta 0
δ
0
) to one another. Calculations are performed at
n
n
n
th order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked cluster theorem and the Hellmann-Feynman theorem, with
n
≤
10
n \leq 10
n
≤
10
. The sole approximation made is to extrapolate such sequences of
n
n
n
th-order results for
M
M
M
to the exact limit,
n
→
∞
n \to \infty
n
→
∞
. By thus locating the points where
M
M
M
vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the
κ
\kappa
κ
--
δ
\delta
δ
half-plane with
κ
>
0
\kappa > 0
κ
>
0
. In particular, we provide the accurate estimate, (
κ
≈
0.547
,
δ
≈
−
0.45
\kappa \approx 0.547,\delta \approx -0.45
κ
≈
0.547
,
δ
≈
−
0.45
), for the position of the quantum triple point (QTP) in the region
δ
<
0
\delta < 0
δ
<
0
. We also show that there is no counterpart of such a QTP in the region
δ
>
0
\delta > 0
δ
>
0
, where the two quasiclassical phase boundaries show instead an ``avoided crossing'' behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected
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Last time updated on 10/08/2019