2,103 research outputs found
Landau Expansion for the Kugel-Khomskii Hamiltonian
The Kugel-Khomskii (KK) Hamiltonian for the titanates describes spin and
orbital superexchange interactions between ions in an ideal perovskite
structure in which the three orbitals are degenerate in energy and
electron hopping is constrained by cubic site symmetry. In this paper we
implement a variational approach to mean-field theory in which each site, ,
has its own single-site density matrix \rhov(i), where , the
number of allowed single-particle states, is 6 (3 orbital times 2 spin states).
The variational free energy from this 35 parameter density matrix is shown to
exhibit the unusual symmetries noted previously which lead to a
wavevector-dependent susceptibility for spins in orbitals which is
dispersionless in the -direction. Thus, for the cubic KK model
itself, mean-field theory does not provide wavevector `selection', in agreement
with rigorous symmetry arguments. We consider the effect of including various
perturbations. When spin-orbit interactions are introduced, the susceptibility
has dispersion in all directions in -space, but the resulting
antiferromagnetic mean-field state is degenerate with respect to global
rotation of the staggered spin, implying that the spin-wave spectrum is
gapless. This possibly surprising conclusion is also consistent with rigorous
symmetry arguments. When next-nearest-neighbor hopping is included, staggered
moments of all orbitals appear, but the sum of these moments is zero, yielding
an exotic state with long-range order without long-range spin order. The effect
of a Hund's rule coupling of sufficient strength is to produce a state with
orbital order.Comment: 20 pages, 5 figures, submitted to Phys. Rev. B (2003
Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder
We investigate the explicit renormalization group for fermionic field
theoretic representation of two-dimensional random bond Ising model with
long-range correlated disorder. We show that a new fixed point appears by
introducing a long-range correlated disorder. Such as the one has been observed
in previous works for the bosonic () description. We have calculated
the correlation length exponent and the anomalous scaling dimension of
fermionic fields at this fixed point. Our results are in agreement with the
extended Harris criterion derived by Weinrib and Halperin.Comment: 5 page
Fictitious fluxes in doped antiferromagnets
In a tight binding model of charged spin-1/2 electrons on a square lattice, a
fully polarized ferromagnetic spin configuration generates an apparent U(1)
flux given by times the skyrmion charge density of the ferromagnetic
order parameter. We show here that for an antiferromagnet, there are two
``fictitious'' magnetic fields, one staggered and one unstaggered. The
staggered topological flux per unit cell can be varied between
with a negligible change in the value of the effective
nearest neighbor coupling constant whereas the magnitude of the unstaggered
flux is strongly coupled to the magnitude of the second neighbor effective
coupling.Comment: RevTeX, 5 pages including 4 figure
Slow Light in Doppler Broadened Two level Systems
We show that the propagation of light in a Doppler broadened medium can be
slowed down considerably eventhough such medium exhibits very flat dispersion.
The slowing down is achieved by the application of a saturating counter
propagating beam that produces a hole in the inhomogeneous line shape. In
atomic vapors, we calculate group indices of the order of 10^3. The
calculations include all coherence effects.Comment: 6 pages, 5 figure
Agronomic practices, major crops and farmers’ perceptions of the importance of good stand establishment in Musikavanhu Communal Area, Zimbabwe
A journal article on Zimbabwe farmers’ perceptions of the importance of good stand establishment.Surveys were conducted of rain-fed crops growing in farmers’ fields in the Musikavanhu Communal Area in Natural Region V of Zimbabwe during and after the 19S5/96 cropping season. The major crops were sorghum, maize and sunflower grown by 94.36 and 15 per cent of the farmers, respectively, and occupied 82.12 and seven per cent of the land. Eleven sorghum cultivars were grown in the area during the 1995/96 season, although only four were grown by more than 10 per cent of the farmers. The most popular maize variety was grown by 28 per cent of farmers on 10 per cent of the land, but had been distributed as part of a drought relief package. Stand establishment was identified as a major crop production constraint in this area. More than 50 percent of the farmers gap-filled at least once and there was a good correlation (R2 = 0.73) between frequency of re-sowing of sorghum and the number of varieties present in fields because seed of the initial, preferred variety was not available for later sowings. On-farm seed priming was fairly common in maize and transplanting, using thinnings, was almost universal in sorghum
Hidden Symmetries and their Consequences in Cubic Perovskites
The five-band Hubbard model for a band with one electron per site is a
model which has very interesting properties when the relevant ions are located
at sites with high (e. g. cubic) symmetry. In that case, if the crystal field
splitting is large one may consider excitations confined to the lowest
threefold degenerate orbital states. When the electron hopping matrix
element () is much smaller than the on-site Coulomb interaction energy
(), the Hubbard model can be mapped onto the well-known effective
Hamiltonian (at order ) derived by Kugel and Khomskii (KK). Recently
we have shown that the KK Hamiltonian does not support long range spin order at
any nonzero temperature due to several novel hidden symmetries that it
possesses. Here we extend our theory to show that these symmetries also apply
to the underlying three-band Hubbard model. Using these symmetries we develop a
rigorous Mermin-Wagner construction, which shows that the three-band Hubbard
model does not support spontaneous long-range spin order at any nonzero
temperature and at any order in -- despite the three-dimensional lattice
structure. Introduction of spin-orbit coupling does allow spin ordering, but
even then the excitation spectrum is gapless due to a subtle continuous
symmetry. Finally we showed that these hidden symmetries dramatically simplify
the numerical exact diagonalization studies of finite clusters.Comment: 26 pages, 3 figures, 520 KB, submitted Phys. Rev.
Order from disorder in lattice QCD at high density
We investigate the properties of the ground state of strong coupling lattice
QCD at finite density. Our starting point is the effective Hamiltonian for
color singlet objects, which looks at lowest order as an antiferromagnet, and
describes meson physics with a fixed baryon number background. We concentrate
on uniform baryon number backgrounds (with the same baryon number on all
sites), for which the ground state was extracted in an earlier work, and
calculate the dispersion relations of the excitations. Two types of Goldstone
boson emerge. The first, antiferromagnetic spin waves, obey a linear dispersion
relation. The others, ferromagnetic magnons, have energies that are quadratic
in their momentum. These energies emerge only when fluctuations around the
large-N_c ground state are taken into account, along the lines of ``order from
disorder'' in frustrated magnetic systems. Unlike other spectrum calculations
in order from disorder, we employ the Euclidean path integral. For comparison,
we also present a Hamiltonian calculation using a generalized
Holstein-Primakoff transformation. The latter can only be constructed for a
subset of the cases we consider.Comment: 24 pages, 6 figures, 1 tabl
Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice
The frequency-moment expansion method is developed to analyze the validity of
the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the
generalized Hubbard model at half filling and large . For the particular
case of the Hubbard model with nearest-neighbor hopping on a triangular lattice
lacking the particle-hole symmetry results reveal substantial violation of the
sum rule.Comment: 4 pages, 2 figure
Ensemble dependence in the Random transverse-field Ising chain
In a disordered system one can either consider a microcanonical ensemble,
where there is a precise constraint on the random variables, or a canonical
ensemble where the variables are chosen according to a distribution without
constraints. We address the question as to whether critical exponents in these
two cases can differ through a detailed study of the random transverse-field
Ising chain. We find that the exponents are the same in both ensembles, though
some critical amplitudes vanish in the microcanonical ensemble for correlations
which span the whole system and are particularly sensitive to the constraint.
This can \textit{appear} as a different exponent. We expect that this apparent
dependence of exponents on ensemble is related to the integrability of the
model, and would not occur in non-integrable models.Comment: 8 pages, 12 figure
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