64 research outputs found
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
Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice
We study the ground state of a spin-half Heisenberg antiferromagnet on the
stacked kagome lattice by using a spin-rotation-invariant Green's-function
method. Since the pure two-dimensional kagome antiferromagnet is most likely a
magnetically disordered quantum spin liquid, we investigate the question
whether the coupling of kagome layers in a stacked three-dimensional system may
lead to a magnetically ordered ground state. We present spin-spin correlation
functions and correlation lengths. For comparison we apply also linear spin
wave theory. Our results provide strong evidence that the system remains
short-range ordered independent of the sign and the strength of the interlayer
coupling
Smooth stable and unstable manifolds for stochastic partial differential equations
Invariant manifolds are fundamental tools for describing and understanding
nonlinear dynamics. In this paper, we present a theory of stable and unstable
manifolds for infinite dimensional random dynamical systems generated by a
class of stochastic partial differential equations. We first show the existence
of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's
method. Then, we prove the smoothness of these invariant manifolds
Criteria for strong and weak random attractors
The theory of random attractors has different notions of attraction, amongst
them pullback attraction and weak attraction. We investigate necessary and
sufficient conditions for the existence of pullback attractors as well as of
weak attractors
Linear independence of localized magnon states
At the magnetic saturation field, certain frustrated lattices have a class of
states known as "localized multi-magnon states" as exact ground states. The
number of these states scales exponentially with the number of spins and
hence they have a finite entropy also in the thermodynamic limit
provided they are sufficiently linearly independent. In this article we present
rigorous results concerning the linear dependence or independence of localized
magnon states and investigate special examples. For large classes of spin
lattices including what we called the orthogonal type and the isolated type as
well as the kagom\'{e}, the checkerboard and the star lattice we have proven
linear independence of all localized multi-magnon states. On the other hand the
pyrochlore lattice provides an example of a spin lattice having localized
multi-magnon states with considerable linear dependence.Comment: 23 pages, 6 figure
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
High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
In this article, we prove that exact representations of dimer and plaquette
valence-bond ket ground states for quantum Heisenberg antiferromagnets may be
formed via the usual coupled cluster method (CCM) from independent-spin product
(e.g. N\'eel) model states. We show that we are able to provide good results
for both the ground-state energy and the sublattice magnetization for dimer and
plaquette valence-bond phases within the CCM. As a first example, we
investigate the spin-half -- model for the linear chain, and we show
that we are able to reproduce exactly the dimerized ground (ket) state at
. The dimerized phase is stable over a range of values for
around 0.5. We present evidence of symmetry breaking by considering
the ket- and bra-state correlation coefficients as a function of . We
then consider the Shastry-Sutherland model and demonstrate that the CCM can
span the correct ground states in both the N\'eel and the dimerized phases.
Finally, we consider a spin-half system with nearest-neighbor bonds for an
underlying lattice corresponding to the magnetic material CaVO (CAVO).
We show that we are able to provide excellent results for the ground-state
energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes
of this model. The exact plaquette and dimer ground states are reproduced by
the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table
Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder
This is a review of ground-state features of the s=1/2 Heisenberg
antiferromagnet on two-dimensional lattices. A central issue is the interplay
of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor
bonds, geometric frustration) and quantum fluctuations and their impact on
possible long-range order. This article presents a unified summary of all 11
two-dimensional uniform Archimedean lattices which include e.g. the square,
triangular and kagome lattice. We find that the ground state of the spin-1/2
Heisenberg antiferromagnet is likely to be semi-classically ordered in most
cases. However, the interplay of geometric frustration and quantum fluctuations
gives rise to a quantum paramagnetic ground state without semi-classical
long-range order on two lattices which are precisely those among the 11 uniform
Archimedean lattices with a highly degenerate ground state in the classical
limit. The first one is the famous kagome lattice where many low-lying singlet
excitations are known to arise in the spin gap. The second lattice is called
star lattice and has a clear gap to all excitations.
Modification of certain bonds leads to quantum phase transitions which are
also discussed briefly. Furthermore, we discuss the magnetization process of
the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on
anomalies like plateaus and a magnetization jump just below the saturation
field. As an illustration we discuss the two-dimensional Shastry-Sutherland
model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review
article. This version corrects two further typographic errors (three total
with respect to the published version), see page 2 for detail
Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets
Using the coupled cluster method we investigate spin- -
Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, triangular
lattice when the spin quantum number or . With respect to a
square-lattice geometry the model has antiferromagnetic () bonds
between nearest neighbours and competing () bonds between
next-nearest neighbours across only one of the diagonals of each square
plaquette, the same one in each square. In a topologically equivalent
triangular-lattice geometry, we have two types of nearest-neighbour bonds:
namely the bonds along parallel chains and the
bonds producing an interchain coupling. The model thus interpolates
between an isotropic HAF on the square lattice at and a set of
decoupled chains at , with the isotropic HAF on the
triangular lattice in between at . For both the and the
models we find a second-order quantum phase transition at
and respectively,
between a N\'{e}el antiferromagnetic state and a helical state. In both cases
the ground-state energy and its first derivative are
continuous at , while the order parameter for the transition
(viz., the average on-site magnetization) does not go to zero on either side of
the transition. The transition at for both the and
cases is analogous to that observed in our previous work for the
case at a value . However, for the higher
spin values the transition is of continuous (second-order) type, as in the
classical case, whereas for the case it appears to be weakly
first-order in nature (although a second-order transition could not be
excluded).Comment: 17 pages, 8 figues (Figs. 2-7 have subfigs. (a)-(d)
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