1,111 research outputs found
Hook formulas for skew shapes III. Multivariate and product formulas
We give new product formulas for the number of standard Young tableaux of
certain skew shapes and for the principal evaluation of the certain Schubert
polynomials. These are proved by utilizing symmetries for evaluations of
factorial Schur functions, extensively studied in the first two papers in the
series "Hook formulas for skew shapes" [arxiv:1512.08348, arxiv:1610.04744]. We
also apply our technology to obtain determinantal and product formulas for the
partition function of certain weighted lozenge tilings, and give various
probabilistic and asymptotic applications.Comment: 40 pages, 17 figures. This is the third paper in the series "Hook
formulas for skew shapes"; v2 added reference to [KO1] (arxiv:1409.1317)
where the formula in Corollary 1.1 had previously appeared; v3 Corollary 5.10
added, resembles published versio
Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet
We study the effect of quantum fluctuations on the half-polarized
magnetization plateau of a pyrochlore antiferromagnet. We argue that an
expansion around the easy axis limit is appropriate for discussing the ground
state selection amongst the classically degenerate manifold of collinear states
with a 3:1 ratio of spins parallel/anti-parallel to the magnetization axis. A
general approach to the necessary degenerate perturbation theory is presented,
and an effective quantum dimer model within this degenerate manifold is derived
for arbitrary spin . We also generalize the existing semiclassical analysis
of Hizi and Henley [Phys. Rev. B {\bf 73}, 054403 (2006)] to the easy axis
limit, and show that both approaches agree at large . We show that under
rather general conditions, the first non-constant terms in the effective
Hamiltonian for occur only at {\sl sixth} order in the transverse
exchange coupling. For , the effective Hamiltonian predicts a
magnetically ordered state. For more exotic possibilities may be
realized, though an analytical solution of the resulting quantum dimer model is
not possible
Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
We propose a general non-perturbative scheme that quantitatively maps the
low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to
effective Generalized Quantum Dimer Models. We develop the formal lattice
independent frame and establish some important results on (i) the locality of
the generated Hamiltonians (ii) how full resummations can be performed in this
renormalization scheme. The method is then applied to the much debated kagome
antiferromagnet for which a fully resummed effective Hamiltonian - shown to
capture the essential properties and provide deep insights on the microscopic
model [D. Poilblanc, M. Mambrini and D. Schwandt, arXiv:0912.0724] - is
derived.Comment: 26 pages, 4 figures, EPAPS inlined, manuscript revised, corrected
minor typos (notably figure 2)
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