29 research outputs found
Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance
To understand the role of local sublattice imbalance in low-energy spectra of
s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor
Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform
many-body calculations using an implementation of the density matrix
renormalization group (DMRG) technique for generic tree graphs. We discover
that the bond-centered Cayley tree has a quasidegenerate set of a low-lying
tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For
understanding the construction of the first excited state from the many-body
ground state, we consider a wave function ansatz given by the single-mode
approximation, which yields a high overlap with the DMRG wave function.
Observing the ground-state entanglement spectrum leads us to a picture of the
low-energy degrees of freedom being "giant spins" arising out of sublattice
imbalance, which helps us analytically understand the scaling of the
finite-size spin gap. The Schwinger-boson mean-field theory has been
generalized to nonuniform lattices, and ground states have been found which are
spatially inhomogeneous in the mean-field parameters.Comment: 19 pages, 12 figures, 6 tables. Changes made to manuscript after
referee suggestions: parts reorganized, clarified discussion on Fibonacci
tree, typos correcte
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
Extinction in lower Hessenberg branching processes with countably many types
We consider a class of branching processes with countably many types which we
refer to as Lower Hessenberg branching processes. These are multitype
Galton-Watson processes with typeset , in which
individuals of type may give birth to offspring of type only.
For this class of processes, we study the set of fixed points of the
progeny generating function. In particular, we highlight the existence of a
continuum of fixed points whose minimum is the global extinction probability
vector and whose maximum is the partial extinction probability
vector . In the case where
, we derive a global extinction
criterion which holds under second moment conditions, and when
we develop necessary and sufficient
conditions for
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
The frustrated spin- -- isotropic model on the honeycomb lattice
We study the zero-temperature ground-state (GS) phase diagram of a spin-half
-- model on the honeycomb lattice with nearest-neighbor
exchange coupling and frustrating next-nearest-neighbor exchange
coupling , where both bonds are of the isotropic
type, using the coupled cluster method. Results are presented for the GS
energy per spin, magnetic order parameter, and staggered dimer valence-bond
crystalline (SDVBC) susceptibility, for values of the frustration parameter in
the range . In this range we find phases exhibiting,
respectively, N\'{e}el planar [N(p)], N\'{e}el -aligned [N()],
SDVBC, and N\'{e}el-II planar [N-II(p)] orderings which break the lattice
rotational symmetry. The N(p) state, which is stable for the classical version
of the model in the range , is found to form
the GS phase out to a first quantum critical point at , beyond which the stable GS phase has N() order over the range
we find a strong competition to form the GS phase between
states with N-II(p) and SDVBC forms of order. Our best estimate, however, is
that the stable GS phase over the range is a mixed state with both SDVBC and N-II(p)
forms of order; and for values is the N-II(p) state,
which is stable at the classical level only at the highly degenerate point
. Over the range we find no evidence
for any of the spiral phases that are present classically for all values
, nor for any quantum spin-liquid state