Chemistry Reference
In-Depth Information
0.20
S
(
Q
)
C
L
/2
0.15
0.10
0.05
0.00
0
0.2
0.4
0.6
1/
L
Figure 12
World-line Monte Carlo results for the square lattice Heisenberg antiferro-
magnet: Structure factor
S
and the long-distance limit
C
of the correlation function as
functions of the linear system size
L.
The intercept on the vertical axis can be used to find
the staggered magnetization. (Taken with permission from Ref. 104.)
clearly that the ground state is antiferromagnetically ordered. In later work,
the staggered magnetization value was further refined by simulations using a
continuous time loop algorithm,
95
giving the value
m
s
ΒΌ
0
:
3083
0
:
0002.
Bilayer Heisenberg Quantum Antiferromagnet
While quantum fluctuations reduce the staggered magnetization of a
single-layer Heisenberg quantum antiferromagnet from its classical value of
1
2
, they are not strong enough to induce a quantum phase transition. As
discussed in the section on Classical Monte Carlo Approaches, the strength
of the quantum fluctuations can be tuned if one considers a system of two
identical, antiferromagnetically coupled layers defined by the bilayer
Hamiltonian of Eq. [20]. If the interlayer coupling
J
?
is large compared to
the in-plane coupling
J
k
, the corresponding spins in the two layers form
magnetically inert singlets. In contrast, for
J
?
J
k
, the system orders antifer-
romagnetically. There is a quantum phase transition between these two phases
at some critical value of the ratio
J
?
=
J
k
.
In the section on Classical Monte Carlo Approaches we used the
quantum-to-classical mapping to discuss the universal critical behavior of
this quantum phase transition and found it to belong to the three-dimensional
classical Heisenberg universality class. However, this approach does not give
