20,066 research outputs found
Locality-preserving allocations Problems and coloured Bin Packing
We study the following problem, introduced by Chung et al. in 2006. We are
given, online or offline, a set of coloured items of different sizes, and wish
to pack them into bins of equal size so that we use few bins in total (at most
times optimal), and that the items of each colour span few bins (at
most times optimal). We call such allocations -approximate. As usual in bin packing problems, we allow additive
constants and consider as the asymptotic performance ratios.
We prove that for \eps>0, if we desire small , no scheme can beat
(1+\eps, \Omega(1/\eps))-approximate allocations and similarly as we desire
small , no scheme can beat (1.69103, 1+\eps)-approximate allocations.
We give offline schemes that come very close to achieving these lower bounds.
For the online case, we prove that no scheme can even achieve
-approximate allocations. However, a small restriction on item
sizes permits a simple online scheme that computes (2+\eps, 1.7)-approximate
allocations
Absence of a true long-range orbital order in a two-leg Kondo ladder
We investigate, through the density-matrix renormalization group and the
Lanczos technique, the possibility of a two-leg Kondo ladder present an
incommensurate orbital order. Our results indicate a staggered short-range
orbital order at half-filling. Away from half-filling our data are consistent
with an incommensurate quasi-long-range orbital order. We also observed that an
interaction between the localized spins enhances the rung-rung current
correlations.Comment: 7 pages, 6 figures, changed the introduction and added some
discussion
Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field
Using the density matrix renormalization group, we investigate the Renyi
entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We
considered the half-odd integer spin-s chains, with s=1/2,3/2 and 5/2, and
periodic and open boundary conditions. In the case of the spin-1/2 chain we
were able to obtain accurate estimates of the new parity exponents
and that gives the power-law decay of the
oscillations of the Renyi entropy for periodic and open boundary
conditions, respectively. We confirm the relations of these exponents with the
Luttinger parameter , as proposed by Calabrese et al. [Phys. Rev. Lett. 104,
095701 (2010)]. Moreover, the predicted periodicity of the oscillating term was
also observed for some non-zero values of the magnetization . We show that
for the amplitudes of the oscillations are quite small, and get
accurate estimates of and become a
challenge. Although our estimates of the new universal exponents
and for the spin-3/2 chain are not so
accurate, they are consistent with the theoretical predictions.Comment: revised version, accepted to PRB. 9 pages, 3 Figures, 4 Table
- …