17,307 research outputs found
Lattice dependence of saturated ferromagnetism in the Hubbard model
We investigate the instability of the saturated ferromagnetic ground state
(Nagaoka state) in the Hubbard model on various lattices in dimensions d=2 and
d=3. A variational resolvent approach is developed for the Nagaoka instability
both for U = infinity and for U < infinity which can easily be evaluated in the
thermodynamic limit on all common lattices. Our results significantly improve
former variational bounds for a possible Nagaoka regime in the ground state
phase diagram of the Hubbard model. We show that a pronounced particle-hole
asymmetry in the density of states and a diverging density of states at the
lower band edge are the most important features in order to stabilize Nagaoka
ferromagnetism, particularly in the low density limit.Comment: Revtex, 18 pages with 18 figures, 7 pages appendices, section on bcc
lattice adde
On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
We explore the conjectured duality between the critical O(N) vector model and
minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free
theory, the conformal partial wave expansion (CPWE) of the four-point function
of the scalar singlet bilinear is reorganized to make it explicitly
crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge
fields. We are able to analytically establish the factorized form of the fusion
coefficients as well as the two-point function coefficient of the HS currents.
We insist in directly computing the free correlators from bulk graphs with the
unconventional branch. The three-point function of the scalar bilinear turns
out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be
precisely related to the CPWs of the boundary dual scalar and its shadow. The
flow in the IR by Legendre transforming at leading 1/N, following the pattern
of double-trace deformations, and the assumption of degeneracy of the hologram
lead to the CPWE of the scalar four-point function at IR. Here we confirm some
previous results, obtained from more involved computations of skeleton graphs,
as well as extend some of them from d=3 to generic dimension 2<d<4.Comment: 22 pages, 5 figure
A Top-Down Account of Linear Canonical Transforms
We contend that what are called Linear Canonical Transforms (LCTs) should be
seen as a part of the theory of unitary irreducible representations of the
'2+1' Lorentz group. The integral kernel representation found by Collins,
Moshinsky and Quesne, and the radial and hyperbolic LCTs introduced thereafter,
belong to the discrete and continuous representation series of the Lorentz
group in its parabolic subgroup reduction. The reduction by the elliptic and
hyperbolic subgroups can also be considered to yield LCTs that act on
functions, discrete or continuous in other Hilbert spaces. We gather the
summation and integration kernels reported by Basu and Wolf when studiying all
discrete, continuous, and mixed representations of the linear group of real matrices. We add some comments on why all should be considered
canonical
Maximal Cuts in Arbitrary Dimension
We develop a systematic procedure for computing maximal unitarity cuts of
multiloop Feynman integrals in arbitrary dimension. Our approach is based on
the Baikov representation in which the structure of the cuts is particularly
simple. We examine several planar and nonplanar integral topologies and
demonstrate that the maximal cut inherits IBPs and dimension shift identities
satisfied by the uncut integral. Furthermore, for the examples we calculated,
we find that the maximal cut functions from different allowed regions, form the
Wronskian matrix of the differential equations on the maximal cut.Comment: typos corrected, more references adde
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