12,173 research outputs found
Low-energy parameters and spin gap of a frustrated spin- Heisenberg antiferromagnet with on the honeycomb lattice
The coupled cluster method is implemented at high orders of approximation to
investigate the zero-temperature phase diagram of the frustrated
spin- ---- antiferromagnet on the honeycomb lattice.
The system has isotropic Heisenberg interactions of strength ,
and between nearest-neighbour, next-nearest-neighbour and
next-next-nearest-neighbour pairs of spins, respectively. We study it in the
case , in the window
that contains the classical tricritical point (at ) of maximal frustration, appropriate to the limiting value of the spin quantum number. We present results for the magnetic
order parameter , the triplet spin gap , the spin stiffness
and the zero-field transverse magnetic susceptibility for the
two collinear quasiclassical antiferromagnetic (AFM) phases with N\'{e}el and
striped order, respectively. Results for and are given for the
three cases , and , while those for
and are given for the two cases and . On
the basis of all these results we find that the spin- and spin-1
models both have an intermediate paramagnetic phase, with no discernible
magnetic long-range order, between the two AFM phases in their phase
diagrams, while for there is a direct transition between them. Accurate
values are found for all of the associated quantum critical points. While the
results also provide strong evidence for the intermediate phase being gapped
for the case , they are less conclusive for the case . On
balance however, at least the transition in the latter case at the striped
phase boundary seems to be to a gapped intermediate state
The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB Approximation Scheme for Lattice Models
A new approximation hierarchy, called the LPSUB scheme, is described for
the coupled cluster method (CCM). It is applicable to systems defined on a
regular spatial lattice. We then apply it to two well-studied prototypical
(spin-1/2 Heisenberg antiferromagnetic) spin-lattice models, namely: the XXZ
and the XY models on the square lattice in two dimensions. Results are obtained
in each case for the ground-state energy, the ground-state sublattice
magnetization and the quantum critical point. They are all in good agreement
with those from such alternative methods as spin-wave theory, series
expansions, quantum Monte Carlo methods and the CCM using the alternative
LSUB and DSUB schemes. Each of the three CCM schemes (LSUB, DSUB
and LPSUB) for use with systems defined on a regular spatial lattice is
shown to have its own advantages in particular applications
Transverse Magnetic Susceptibility of a Frustrated Spin- ---- Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice
We use the coupled cluster method (CCM) to study a frustrated
spin- ---- Heisenberg antiferromagnet
on a bilayer honeycomb lattice with stacking. Both nearest-neighbor (NN)
and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange
interactions are present in each layer, with respective exchange coupling
constants and . The two layers are
coupled with NN AFM exchanges with coupling strength . We calculate to high orders of approximation within the CCM
the zero-field transverse magnetic susceptibility in the N\'eel phase.
We thus obtain an accurate estimate of the full boundary of the N\'eel phase in
the plane for the zero-temperature quantum phase diagram. We
demonstrate explicitly that the phase boundary derived from is fully
consistent with that obtained from the vanishing of the N\'eel magnetic order
parameter. We thus conclude that at all points along the N\'eel phase boundary
quasiclassical magnetic order gives way to a nonclassical paramagnetic phase
with a nonzero energy gap. The N\'eel phase boundary exhibits a marked
reentrant behavior, which we discuss in detail
Collinear antiferromagnetic phases of a frustrated spin- ---- Heisenberg model on an -stacked bilayer honeycomb lattice
The zero-temperature quantum phase diagram of the spin-
---- model on an -stacked bilayer honeycomb
lattice is investigated using the coupled cluster method (CCM). The model
comprises two monolayers in each of which the spins, residing on
honeycomb-lattice sites, interact via both nearest-neighbor (NN) and
frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg
exchange iteractions, with respective strengths and . The two layers are coupled via a comparable Heisenberg
exchange interaction between NN interlayer pairs, with a strength
. The complete phase boundaries of two
quasiclassical collinear AFM phases, namely the N\'{e}el and N\'{e}el-II
phases, are calculated in the half-plane with .
Whereas on each monolayer in the N\'{e}el state all NN pairs of spins are
antiparallel, in the N\'{e}el-II state NN pairs of spins on zigzag chains along
one of the three equivalent honeycomb-lattice directions are antiparallel,
while NN interchain spins are parallel. We calculate directly in the
thermodynamic (infinite-lattice) limit both the magnetic order parameter
and the excitation energy from the ground state to the
lowest-lying excited state (where is the total
component of spin for the system as a whole, and where the collinear ordering
lies along the direction) for both quasiclassical states used (separately)
as the CCM model state, on top of which the multispin quantum correlations are
then calculated to high orders () in a systematic series of
approximations involving -spin clusters. The sole approximation made is then
to extrapolate the sequences of th-order results for and to the
exact limit,
A high-order study of the quantum critical behavior of a frustrated spin- antiferromagnet on a stacked honeycomb bilayer
We study a frustrated spin-
------ Heisenberg antiferromagnet on an
-stacked bilayer honeycomb lattice. In each layer we consider
nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor
antiferromagnetic (AFM) exchange couplings , , and ,
respectively. The two layers are coupled with an AFM NN exchange coupling
. The model is studied for arbitrary values of
along the line that includes the most
highly frustrated point at , where the classical ground
state is macroscopically degenerate. The coupled cluster method is used at high
orders of approximation to calculate the magnetic order parameter and the
triplet spin gap. We are thereby able to give an accurate description of the
quantum phase diagram of the model in the plane in the window , . This includes two AFM phases with
N\'eel and striped order, and an intermediate gapped paramagnetic phase that
exhibits various forms of valence-bond crystalline order. We obtain accurate
estimations of the two phase boundaries, , or
equivalently, , with (N\'eel) and 2
(striped). The two boundaries exhibit an "avoided crossing" behavior with both
curves being reentrant
Ground-state phases of the spin-1 -- Heisenberg antiferromagnet on the honeycomb lattice
We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg
antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange
coupling and frustrating next-nearest-neighbor coupling , using the coupled cluster method implemented to high orders
of approximation, and based on model states with different forms of classical
magnetic order. For each we calculate directly in the bulk thermodynamic limit
both ground-state low-energy parameters (including the energy per spin,
magnetic order parameter, spin stiffness coefficient, and zero-field uniform
transverse magnetic susceptibility) and their generalized susceptibilities to
various forms of valence-bond crystalline (VBC) order, as well as the energy
gap to the lowest-lying spin-triplet excitation. In the range
we find evidence for four distinct phases. Two of these are quasiclassical
phases with antiferromagnetic long-range order, one with 2-sublattice N\'{e}el
order for , and another with 4-sublattice
N\'{e}el-II order for . Two different
paramagnetic phases are found to exist in the intermediate region. Over the
range we find a gapless
phase with no discernible magnetic order, which is a strong candidate for being
a quantum spin liquid, while over the range we find a gapped phase, which is most likely a lattice nematic
with staggered dimer VBC order that breaks the lattice rotational symmetry
Large- expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number
The coupled cluster method (CCM) is employed to very high orders of
approximation to study the ground-state (GS) properties of the spin-
Heisenberg antiferromagnet (with isotropic interactions, all of equal strength,
between nearest-neighbour pairs only) on the honeycomb lattice. We calculate
with high accuracy the complete set of GS parameters that fully describes the
low-energy behaviour of the system, in terms of an effective magnon field
theory, viz., the energy per spin, the magnetic order parameter (i.e., the
sublattie magnetization), the spin stiffness and the zero-field (uniform,
transverse) magnetic susceptibility, for all values of the spin quantum number
in the range . The CCM data points are
used to calculate the leading quantum corrections to the classical () values of these low-energy parameters, considered as
large- asymptotic expansions
Spin-gap study of the spin- -- model on the triangular lattice
We use the coupled cluster method implemented at high orders of approximation
to study the spin- -- model on the triangular
lattice with Heisenberg interactions between nearest-neighbour and
next-nearest-neighbour pairs of spins, with coupling strengths and
, respectively. In the window we find that the 3-sublattice 120 N\'{e}el-ordered and
2-sublattice 180 stripe-ordered antiferromagnetic states form the
stable ground-state phases in the regions
and , respectively. The spin-triplet gap is
found to vanish over essentially the entire region of the intermediate phase
Ground-state phase structure of the spin- anisotropic planar pyrochlore
We study the zero-temperature ground-state (GS) properties of the
spin- anisotropic planar pyrochlore, using the coupled cluster
method (CCM) implemented to high orders of approximation. The system comprises
a -- model on the checkerboard lattice, with isotropic Heisenberg
interactions of strength between all nearest-neighbour pairs of spins
on the square lattice, and of strength between half of the
next-nearest-neighbour pairs (in the checkerboard pattern). We calculate
results for the GS energy and average local GS on-site magnetization, using
various antiferromagnetic classical ground states as CCM model states. We also
give results for the susceptibility of one of these states against the
formation of crossed-dimer valence-bond crystalline (CDVBC) ordering. The
complete GS phase diagram is presented for arbitrary values of the frustration
parameter , and when each of the exchange couplings
can take either sign
Diplomas for Learning, not Seat Time: The Impacts of New York Regents Examinations
[Excerpt] New York State has been administering curriculum-based Regents Examinations to high school students ever since June 1878. As Sherman Tinkelman, Assistant Commissioner for Examinations and Scholarships described in a 1966 report: The Regents examinations are closely related to the curriculum in New York State. They are, as you can see, inseparably intertwined. One supports and reinforces the other.... These instruments presuppose and define standards.... They are a strong supervisory and instructional tool-- and deliberately so. They are effective in stimulating good teaching and good learning practices (Tinkelman, 1966 p. 12)
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