426,418 research outputs found
A first cubic upper bound on the local reachability index for some positive 2-D systems
[EN] The calculation of the smallest number of steps needed to deterministically reach all local states of an nth-order positive 2-D system, which is called local reachability index (ILR) of that system, was recently tackled bymeans of the use of a suitable composition table. The greatest index ILR obtained in the previous literature was n+3 ([n/2]) 2 for some appropriated values of n. Taking as a basis both a combinatorial approach of such systems and the construction of suitable geometric sets in the plane, an upper bound on ILR depending on the dimension n for a new family of systems is characterized. The 2-D influence digraph of this family of order n = 6 consists of two subdigraphs corresponding to a unique source s. The first one is a cycle involving the first n(1) vertices and is connected to the another subdigraph through the 1-arc (2, n(1) +n(2)), being the natural numbers n(1) and n(2) such that n(1) > n(2) = 2 and n-n(1)-n(2) = 1. The second one has two main cycles, a cycle where only the remaining vertices n(1)+1,..., n appear and a cycle containing only the vertices n(1)+1, n(1)+n(2)-1. Moreover, the last vertices are connected through the 2-arc (n(1) +n(2)-1, n). Furthermore, if n > 12 and is a multiple of 3, for appropriate n(1) and n(2), the ILR of that family is at least cubic, exactly, it must be n(3)+9n(2)+45n+108/27, which shows that some local states can be deterministically reached much further than initially proposed in the literature.We are gratefully thankful to the reviewers for their valuable remarks. This work has been partially supported by the European Union [FEDER funds] and Ministerio de Ciencia e Innovacion through Grants MTM-2013-43678-P and DPI2016-78831-C2-1-R.Bailo Ballarín, E.; Gelonch, J.; Romero Vivó, S. (2019). A first cubic upper bound on the local reachability index for some positive 2-D systems. 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Single and Many Particle Correlation Functions and Uniform Phase Bases for Strongly Correlated Systems
The need for suitable many or infinite fermion correlation functions to
describe some low dimensional strongly correlated systems is discussed. This is
linked to the need for a correlated basis, in which the ground state may be
postive definite, and in which single particle correlations may suffice. A
particular trial basis is proposed, and applied to a certain quasi-1D model.
The model is a strip of the 2D square lattice wrapped around a cylinder, and is
related to the ladder geometries, but with periodic instead of open boundary
conditions along the edges. Analysis involves a novel mean-field approach and
exact diagonalisation. The model has a paramagnetic region and a Nagaoka
ferromagnetic region. The proposed basis is well suited to the model, and
single particle correlations in it have power law decay for the paramagnet,
where the charge motion is qualitatively hard core bosonic. The mean field also
leads to a BCS-type model with single particle long range order.Comment: 23 pages, in plain tex, 12 Postscript figures included. Accepted for
publication in J.Physics : Condensed Matte
Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
We present a general scheme for the calculation of the Renyi entropy of a
subsystem in quantum many-body models that can be efficiently simulated via
quantum Monte Carlo. When the simulation is performed at very low temperature,
the above approach delivers the entanglement Renyi entropy of the subsystem,
and it allows to explore the crossover to the thermal Renyi entropy as the
temperature is increased. We implement this scheme explicitly within the
Stochastic Series expansion as well as within path-integral Monte Carlo, and
apply it to quantum spin and quantum rotor models. In the case of quantum
spins, we show that relevant models in two dimensions with reduced symmetry (XX
model or hardcore bosons, transverse-field Ising model at the quantum critical
point) exhibit an area law for the scaling of the entanglement entropy.Comment: 5+1 pages, 4+1 figure
Pattern formation in systems with competing interactions
There is a growing interest, inspired by advances in technology, in the low
temperature physics of thin films. These quasi-2D systems show a wide range of
ordering effects including formation of striped states, reorientation
transitions, bubble formation in strong magnetic fields, etc. The origins of
these phenomena are, in many cases, traced to competition between short ranged
exchange ferromagnetic interactions, favoring a homogeneous ordered state, and
the long ranged dipole-dipole interaction, which opposes such ordering on the
scale of the whole sample. The present theoretical understanding of these
phenomena is based on a combination of variational methods and a variety of
approximations, e.g., mean-field and spin-wave theory. The comparison between
the predictions of these approximate methods and the results of MonteCarlo
simulations are often difficult because of the slow relaxation dynamics
associated with the long-range nature of the dipole-dipole interactions. In
this note we will review recent work where we prove existence of periodic
structures in some lattice and continuum model systems with competing
interactions. The continuum models have also been used to describe
micromagnets, diblock polymers, etc.Comment: 11 pages, 1 figure, to appear in the AIP conference proceedings of
the 10th Granada Seminar on Computational Physics, Sept. 15-19, 2008. (v2)
Updated reference
Absence of Localization in Certain Field Effect Transistors
We review some experimental and theoretical results on the metal-to-insulator
transition (MIT) observed at zero magnetic field (B=0) in several
two-dimensional electron systems (2DES). Scaling of the conductance and
magnetic field dependence of the conductance provide convincing evidence that
the MIT is driven by Coulomb interactions among the carriers and is
dramatically sensitive to spin polarization of the carriers.Comment: 8 pages, LaTeX, figure label change
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