1,672 research outputs found
Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
We study the ground state properties of the critical Lipkin-Meshkov-Glick
model. Using the Holstein-Primakoff boson representation, and the continuous
unitary transformation technique, we compute explicitly the finite-size scaling
exponents for the energy gap, the ground state energy, the magnetization, and
the spin-spin correlation functions. Finally, we discuss the behavior of the
two-spin entanglement in the vicinity of the phase transition.Comment: 4 pages, published versio
Emergent Fermions and Anyons in the Kitaev Model
We study the gapped phase of the Kitaev model on the honeycomb lattice using
perturbative continuous unitary transformations. The effective low-energy
Hamiltonian is found to be an extended toric code with interacting anyons.
High-energy excitations are emerging free fermions which are composed of
hardcore bosons with an attached string of spin operators. The excitation
spectrum is mapped onto that of a single particle hopping on a square lattice
in a magnetic field. We also illustrate how to compute correlation functions in
this framework. The present approach yields analytical perturbative results in
the thermodynamical limit without using the Majorana or the Jordan-Wigner
fermionization initially proposed to solve this problem.Comment: 4 pages, 5 figures, published versio
Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows
Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are
increasingly popular and attractive methods that propose efficient multiphase
formulations, each one with its own strengths and weaknesses. In this context,
when it comes to study a given multi-fluid problem, it is helpful to rely on a
quantitative comparison to decide which approach should be used and in which
context. In particular, the simulation of intermittent two-phase flows in pipes
such as slug flows is a complex problem involving moving and intersecting
interfaces for which both SPH and LBM could be considered. It is a problem of
interest in petroleum applications since the formation of slug flows that can
occur in submarine pipelines connecting the wells to the production facility
can cause undesired behaviors with hazardous consequences. In this work, we
compare SPH and LBM multiphase formulations where surface tension effects are
modeled respectively using the continuum surface force and the color gradient
approaches on a collection of standard test cases, and on the simulation of
intermittent flows in 2D. This paper aims to highlight the contributions and
limitations of SPH and LBM when applied to these problems. First, we compare
our implementations on static bubble problems with different density and
viscosity ratios. Then, we focus on gravity driven simulations of slug flows in
pipes for several Reynolds numbers. Finally, we conclude with simulations of
slug flows with inlet/outlet boundary conditions. According to the results
presented in this study, we confirm that the SPH approach is more robust and
versatile whereas the LBM formulation is more accurate and faster
Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
We analyze the Kitaev model on the triangle-honeycomb lattice whose ground
state has recently been shown to be a chiral spin liquid. We consider two
perturbative expansions: the isolated-dimer limit containing Abelian anyons and
the isolated-triangle limit. In the former case, we derive the low-energy
effective theory and discuss the role played by multi-plaquette interactions.
In this phase, we also compute the spin-spin correlation functions for any
vortex configuration. In the isolated-triangle limit, we show that the
effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at
the isotropic point. We also compute the next-order correction which opens a
gap and yields non-Abelian anyons.Comment: 7 pages, 4 figures, published versio
Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick
model by means of the Holstein-Primakoff representation of the spin operators
and the continuous unitary transformations method. This combination allows us
to compute analytically leading corrections to the ground state energy, the
gap, the magnetization, and the two-spin correlation functions. We also present
numerical calculations for large system size which confirm the validity of this
approach. Finally, we use these results to discuss the entanglement properties
of the ground state focusing on the (rescaled) concurrence that we compute in
the thermodynamical limit.Comment: 20 pages, 9 figures, published versio
Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
We establish a relation between several entanglement properties in the
Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins
embedded in a magnetic field. We provide analytical proofs that the single-copy
entanglement and the global geometric entanglement of the ground state close to
and at criticality behave as the entanglement entropy. These results are in
deep contrast to what is found in one- dimensional spin systems where these
three entanglement measures behave differently.Comment: 4 pages, 2 figures, published versio
Finite-size scaling exponents and entanglement in the two-level BCS model
We analyze the finite-size properties of the two-level BCS model. Using the
continuous unitary transformation technique, we show that nontrivial scaling
exponents arise at the quantum critical point for various observables such as
the magnetization or the spin-spin correlation functions. We also discuss the
entanglement properties of the ground state through the concurrence which
appears to be singular at the transition.Comment: 4 pages, 3 figures, published versio
Tables de transposition pour la satisfaction de contraintes
Dans ce papier, nous proposons une approche basée sur la reconnaissance d'états dans le cadre de la résolution du problème de satisfaction de contraintes (CSP). L'idée principale consiste en la mémorisation d'états pendant la recherche de manière à prévenir la résolution de sous-réseaux similaires. Les techniques classiques évitent la réapparition de conflits précédemment rencontrés en enregistrant des ensembles conflits (conflict sets). Ceci contraste avec notre approche basée sur les états qui mémorise des sous-réseaux déjà explorés, c'est à dire une photographie de certains domaines sélectionnés. Ces informations sont ensuite exploitées pour éviter soit le parcours d'états in consistants, soit de recalculer l'ensemble des solutions de ces sous-réseaux. Les deux approches présentent une certaine complémentarité : en effet différents états peuvent être évités à partir d'une même instantiation partielle ou ensemble conflits tandis que différentes instantiations partielles peuvent mener à un même état qui n'a besoin d'être exploré qu'une seule fois. De plus notre méthode permet de détecter et casser dynamiquement certaines formes de symétries (notamment l'interchangeabilité au voisinage). Les résultats expérimentaux obtenus laissent entrevoir des perspectives promette uses pour la recherche basée sur les états
Recherche dirigée par le dernier conflit
Dans ce papier, nous proposons une nouvelle approche pour guider la recherche vers la source des conflits. Son principe est le suivant : après chaque conflit, la dernière variable assignée est sélectionnée en priorité tant que le réseau de contraintes est inconsistant. Ceci permet de découvrir la variable coupable la plus récente (i.e. à l'origine de l'échec) en remontant la branche courante de la feuille vers la racine de l'arbre de recherche. Autrement dit, l'heuristique de choix de variables est violée jusqu'au moment où un retour-arrière sur la variable coupable est effectué et que l'on découvre une valeur singleton consistante. En conséquence, ce type de raisonnement, qui représente un moyen original d'éviter le thrashing, peut facilement être intégré à de nombreux algorithmes de recherche. Les expérimentations effectuées sur un large éventail d'instances démontrent l'efficacité de cette approche
Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
We analyze the properties of low-energy bound states in the transverse-field
Ising model and in the XXZ model on the square lattice. To this end, we develop
an optimized implementation of perturbative continuous unitary transformations.
The Ising model is studied in the small-field limit which is found to be a
special case of the toric code model in a magnetic field. To analyze the XXZ
model, we perform a perturbative expansion about the Ising limit in order to
discuss the fate of the elementary magnon excitations when approaching the
Heisenberg point.Comment: 21 pages, 18 figures, published versio
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