10,849 research outputs found
Phase Transitions in the Spin-Half J_1--J_2 Model
The coupled cluster method (CCM) is a well-known method of quantum many-body
theory, and here we present an application of the CCM to the spin-half J_1--J_2
quantum spin model with nearest- and next-nearest-neighbour interactions on the
linear chain and the square lattice. We present new results for ground-state
expectation values of such quantities as the energy and the sublattice
magnetisation. The presence of critical points in the solution of the CCM
equations, which are associated with phase transitions in the real system, is
investigated. Completely distinct from the investigation of the critical
points, we also make a link between the expansion coefficients of the
ground-state wave function in terms of an Ising basis and the CCM ket-state
correlation coefficients. We are thus able to present evidence of the
breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which
is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any
bipartite lattice. For the square lattice, our best estimates of the points at
which the sign rule breaks down and at which the phase transition from the
antiferromagnetic phase to the frustrated phase occurs are, respectively, given
(to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure
Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems
We study a square-lattice spin-half Heisenberg model where frustration is
introduced by competing nearest-neighbor bonds of different signs. We discuss
the influence of quantum fluctuations on the nature of the zero-temperature
phase transitions from phases with collinear magnetic order at small
frustration to phases with noncollinear spiral order at large frustration. We
use the coupled cluster method (CCM) for high orders of approximation (up to
LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to
calculate ground-state properties. The role of quantum fluctuations is examined
by comparing the ferromagnetic-spiral and the antiferromagnetic-spiral
transition within the same model. We find clear evidence that quantum
fluctuations prefer collinear order and that they may favour a first order
transition instead of a second order transition in case of no quantum
fluctuations.Comment: 6 pages, 6 Postscipt figures; Accepted for publication in Phys. Rev.
High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model
In this article, we present new results of high-order coupled cluster method
(CCM) calculations, based on a N\'eel model state with spins aligned in the
-direction, for both the ground- and excited-state properties of the
spin-half {\it XXZ} model on the linear chain, the square lattice, and the
simple cubic lattice. In particular, the high-order CCM formalism is extended
to treat the excited states of lattice quantum spin systems for the first time.
Completely new results for the excitation energy gap of the spin-half {\it XXZ}
model for these lattices are thus determined. These high-order calculations are
based on a localised approximation scheme called the LSUB scheme in which we
retain all -body correlations defined on all possible locales of
adjacent lattice sites (). The ``raw'' CCM LSUB results are seen to
provide very good results for the ground-state energy, sublattice
magnetisation, and the value of the lowest-lying excitation energy for each of
these systems. However, in order to obtain even better results, two types of
extrapolation scheme of the LSUB results to the limit (i.e.,
the exact solution in the thermodynamic limit) are presented. The extrapolated
results provide extremely accurate results for the ground- and excited-state
properties of these systems across a wide range of values of the anisotropy
parameter.Comment: 31 Pages, 5 Figure
Continuum coupled cluster expansion
We review the basics of the coupled-cluster expansion formalism for numerical
solutions of the many-body problem, and we outline the principles of an
approach directed towards an adequate inclusion of continuum effects in the
associated single-energy spectrum. We illustrate our findings by considering
the simple case of a single-particle quantum mechanics problem.Comment: 16 pages, 1 figur
The ac-Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice
By means of numerical simulations, we demonstrate that ac field can support
stably moving collective nonlinear excitations in the form of dislocations
(topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with
weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys.
Rev. B{\bf 43}, 11539 (1991)]. Direct generation of the moving dislocations
turns out to be virtually impossible; however, they can be generated initially
in the lattice subject to an auxiliary spatial modulation of the on-site
potential strength. Gradually relaxing the modulation, we are able to get the
stable moving dislocations in the uniform FK lattice with the periodic boundary
conditions, provided that the driving frequency is close to the gap frequency
of the linear excitations in the uniform lattice. The excitations have a large
and noninteger index of commensurability with the lattice (suggesting that its
actual value is irrational). The simulations reveal two different types of the
moving dislocations: broad ones, that extend, roughly, to half the full length
of the periodic lattice (in that sense, they cannot be called solitons), and
localized soliton-like dislocations, that can be found in an excited state,
demonstrating strong persistent internal vibrations. The minimum (threshold)
amplitude of the driving force necessary to support the traveling excitation is
found as a function of the friction coefficient. Its extrapolation suggests
that the threshold does not vanish at the zero friction, which may be explained
by radiation losses. The moving dislocation can be observed experimentally in
an array of coupled small Josephson junctions in the form of an {\it inverse
Josephson effect}, i.e., a dc-voltage response to the uniformly applied ac bias
current.Comment: Plain Latex, 13 pages + 9 PostScript figures. to appear on Journal of
Physics: condensed matte
General relativistic null-cone evolutions with a high-order scheme
We present a high-order scheme for solving the full non-linear Einstein
equations on characteristic null hypersurfaces using the framework established
by Bondi and Sachs. This formalism allows asymptotically flat spaces to be
represented on a finite, compactified grid, and is thus ideal for far-field
studies of gravitational radiation. We have designed an algorithm based on
4th-order radial integration and finite differencing, and a spectral
representation of angular components. The scheme can offer significantly more
accuracy with relatively low computational cost compared to previous methods as
a result of the higher-order discretization. Based on a newly implemented code,
we show that the new numerical scheme remains stable and is convergent at the
expected order of accuracy.Comment: 24 pages, 3 figure
Complete phase diagram of the spin-1/2 -- model (with ) on the honeycomb lattice
We use the coupled cluster method to investigate the ground-state (GS)
properties of the frustrated spin-1/2 -- model on the
honeycomb lattice, with nearest-neighbor exchange coupling plus
next-nearest-neighbor () and next-next-nearest-neighbor () exchanges
of equal strength. In particular we find a direct first-order phase transition
between the N\'eel-ordered antiferromagnetic phase and the ferromagnetic phase
at a value when , compared to the
corresponding classical value of -1. We find no evidence for any intermediate
phase. From this and our previous CCM studies of the model we present its full
zero-temperature GS phase diagram.Comment: 4 pages, 4 figure
A coupled-cluster study of the ground-state energy and properties of an anisotropic quantum spin lattice model exhibiting antiferromagnetism in various phases
- …