57 research outputs found
Influence of the spin quantum number on the zero-temperature phase transition in the square lattice - model
We investigate the phase diagram of the Heisenberg antiferromagnet on the
square lattice with two different nearest-neighbor bonds and (-
model) at zero temperature. The model exhibits a quantum phase transition at a
critical value between a semi-classically ordered N\'eel and a
magnetically disordered quantum paramagnetic phase of valence-bond type, which
is driven by local singlet formation on bonds. We study the influence of
spin quantum number on this phase transition by means of a variational
mean-field approach, the coupled cluster method, and the Lanczos
exact-diagonalization technique. We present evidence that the critical value
increases with growing according to .Comment: 13 pages, 6 figure
Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum -- model on the square lattice
We study the zero-temperature phase diagram of the
-- Heisenberg model for spin-1 particles on an
infinite square lattice interacting via nearest-neighbour () and
next-nearest-neighbour () bonds. Both bonds have the same -type
anisotropy in spin space. The effects on the quasiclassical N\'{e}el-ordered
and collinear stripe-ordered states of varying the anisotropy parameter
is investigated using the coupled cluster method carried out to high
orders. By contrast with the spin-1/2 case studied previously, we predict no
intermediate disordered phase between the N\'{e}el and collinear stripe phases,
for any value of the frustration , for either the -aligned () or -planar-aligned () states. The quantum phase
transition is determined to be first-order for all values of and
. The position of the phase boundary is determined
accurately. It is observed to deviate most from its classical position (for all values of ) at the Heisenberg isotropic point
(), where . By contrast, at the XY
isotropic point (), we find . In the
Ising limit () as expected.Comment: 20 pages, 5 figure
Quantum -- antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
Using the coupled-cluster method (CCM) and the rotation-invariant Green's
function method (RGM), we study the influence of the interlayer coupling
on the magnetic ordering in the ground state of the spin-1/2
- frustrated Heisenberg antiferromagnet (- model) on the
stacked square lattice. In agreement with known results for the -
model on the strictly two-dimensional square lattice () we find that
the phases with magnetic long-range order at small and large
are separated by a magnetically disordered (quantum
paramagnetic) ground-state phase. Increasing the interlayer coupling
the parameter region of this phase decreases, and, finally, the
quantum paramagnetic phase disappears for quite small .Comment: 4 pages, 3 figure
The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A variational method study
The phase transition of the quantum spin-1/2 frustrated Heisenberg
antiferroferromagnet on an anisotropic square lattice is studied by using a
variational treatment. The model is described by the Heisenberg Hamiltonian
with two antiferromagnetic interactions: nearest-neighbor (NN) with different
coupling strengths J_{1} and J_{1'} along x and y directions competing with a
next-nearest-neighbor coupling J_{2} (NNN). The ground state phase diagram in
the ({\lambda},{\alpha}) space, where {\lambda}=J_{1'}/J_{1} and
{\alpha}=J_{2}/J_{1}, is obtained. Depending on the values of {\lambda} and
{\alpha}, we obtain three different states: antiferromagnetic (AF), collinear
antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate
region {\lambda}_{1}<{\lambda}<1 we observe a QP state between the ordered AF
and CAF phases, which disappears for {\lambda} above some critical value
{\lambda}_{1}. The boundaries between these ordered phases merge at the quantum
critical endpoint (QCE). Below this QCE there is again a direct first-order
transition between the AF and CAF phases, with a behavior approximately
described by the classical line {\alpha}_{c}{\simeq}{\lambda}/2
The ground-state magnetic ordering of the spin-1/2 frustrated J1-J2 XXZ model on the square lattice
Using the coupled-cluster method for infinite lattices and the exact
diagonalization method for finite lattices, we study the influence of an
exchange anisotropy Delta on the ground-state phase diagram of the spin-1/2
frustrated J1-J2 XXZ antiferromagnet on the square lattice. We find that
increasing Delta>1 (i.e. an Ising type easy-axis anisotropy) as well as
decreasing Delta<1 (i.e. an XY type easy-plane anisotropy) both lead to a
monotonic shrinking of the parameter region of the magnetically disordered
quantum phase. Finally, at Delta~1.9 this quantum phase disappears, whereas in
pure XY limit (Delta=0) there is still a narrow region around J2 =0.5J1 where
the quantum paramagnetic ground-state phase exists.Comment: 4 pages, 6 figures, paper accepted for the proceedings of the
conference HFM 200
The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
We investigate the ground-state magnetic order of the spin-1/2 J1-J2
Heisenberg model on the square lattice with ferromagnetic nearest-neighbor
exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange
J2>0. We use the coupled-cluster method to high orders of approximation and
Lanczos exact diagonalization of finite lattices of up to N=40 sites in order
to calculate the ground-state energy, the spin-spin correlation functions, and
the magnetic order parameter. We find that the transition point at which the
ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1| (exact
diagonalization) and J2^{c1}=0.394|J1| (coupled-cluster method). We compare our
results for ferromagnetic J1 with established results for the spin-1/2 J1-J2
Heisenberg model with antiferromagnetic J1. We find that both models (i.e.,
ferro- and antiferromagnetic J1) behave similarly for large J2, although
significant differences between them are observed for J2/|J1| \lesssim 0.6.
Although the semiclassical collinear magnetic long-range order breaks down at
J2^{c2} \approx 0.6J1 for antiferromagnetic J1, we do not find a similar
breakdown of this kind of long-range order until J2 \sim 0.4|J1| for the model
with ferromagnetic J1. Unlike the case for antiferromagnetic J1, if an
intermediate disordered phase does occur between the phases exhibiting
semiclassical collinear stripe order and ferromagnetic order for ferromagnetic
J1 then it is likely to be over a very small range below J2 \sim 0.4|J1|.Comment: 15 pages, 7 figures, 2 table
A frustrated quantum spin-{\boldmath s} model on the Union Jack lattice with spins {\boldmath s>1/2}
The zero-temperature phase diagrams of a two-dimensional frustrated quantum
antiferromagnetic system, namely the Union Jack model, are studied using the
coupled cluster method (CCM) for the two cases when the lattice spins have spin
quantum number and . The system is defined on a square lattice and
the spins interact via isotropic Heisenberg interactions such that all
nearest-neighbour (NN) exchange bonds are present with identical strength
, and only half of the next-nearest-neighbour (NNN) exchange bonds are
present with identical strength . The bonds are
arranged such that on the unit cell they form the pattern of the
Union Jack flag. Clearly, the NN bonds by themselves (viz., with )
produce an antiferromagnetic N\'{e}el-ordered phase, but as the relative
strength of the frustrating NNN bonds is increased a phase transition
occurs in the classical case () at to a canted ferrimagnetic phase. In the quantum cases considered
here we also find strong evidence for a corresponding phase transition between
a N\'{e}el-ordered phase and a quantum canted ferrimagnetic phase at a critical
coupling for and for . In both cases the ground-state energy and its first
derivative seem continuous, thus providing a typical scenario of a
second-order phase transition at , although the order
parameter for the transition (viz., the average ground-state on-site
magnetization) does not go to zero there on either side of the transition.Comment: 1
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