Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic N\'eel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.Comment: 23 pages, 8 figure

Genes and Ant for Defaults Logic

Default Logic and Logic Programming with stable model semantics are recognized as powerful frameworks for incomplete information representation. Their expressive power are suitable for non monotonic reasoning, but the counterpart is their very high level of theoretical complexity. The purpose of this paper is to show how heuristics issued from combinatorial optimization and operation research can be used to built non monotonic reasonning systems

Une nouvelle stratégie de mise sous forme prénexe pour des formules booléennes quantifiées avec bi-implications

La plupart des procédures pour résoudre le problème de validitédes formules booléennes quantifiées prennent en entrée seulement des formules sous forme normale négative, voire sous forme normale conjonctive, et donc prénexes. Mais, il est rarement naturel d’exprimer un problème directement sous cette forme. Par exemple, en spécification, des symboles propositionnels existentiellement quantifiés sont insérés, selon un même motif, pour capturer des résultats intermédiaires. Ainsi, pour pouvoir utiliser les solveurs de l’état de l’art, il est nécessaire de convertir toute formule booléenne quantifiée sous forme prénexe. Un problème majeur de cette mise sous forme prénexe est qu’elle détruit complètement la structure originale de la formule. De plus, lors de la mise sous forme prénexe des bi-implications il y a duplication de leurs sous-formules, ceci incluant les quantificateurs. Cela conduit généralement à une croissance exponentielle de la taille de la formule. Dans ce travail, nous nous focalisons sur le motif très courant des résultats intermédiaires. Nous mettons en évidence des équivalences logiques qui permettent d’extraire les sous-formules améliorant ainsi nettement les performances des solveurs de l’état de l’art

From (Quantified) Boolean Formulae to Answer Set Programming

We propose in this article a translation from quantified Boolean formulae to answer set programming. The computation of a solution of a quantified Boolean formula is then equivalent to the computation of a stable model for a normal logic program. The case of unquantified Boolean formulae is also considered since it is equivalent to the case of quantified Boolean formulae with only existential quantifiers

A New Prenexing Strategy for Quantified Boolean Formulae with Bi-Implications

Most of the recent and effcient decision pro cedures for quan-tified Bo olean formulae accept formulae in negation normal form as input or in an even more restrictive format such conjunctive normal form. But real problems are rarely expressed in such forms. For instance, in specification, intermediate prop ositional symb ols are used to capture lo cal results with always the same pattern. So, in order to use most of the state-of-the-art solvers the original formula has firstly to b e converted in prenex form. A drawback of this preliminary step is to destroy completely the original structures of the formula. Furthermore, during the prenexing pro cess, bi-implications are translated in such a way that there is a du- plication of their sub-formulae including the quantifiers. In general, this pro cess leads to an exp onential growth of the formula. In this work, we fo cus on this very common pattern of intermediate result. We intro duce new logical equivalences allowing us to extract these sub-formulae in a way that can improve the p erformance of the state-of-the-art quantified Boolean solver

From (Quantified) Boolean Formulas to Answer Set Programming

We propose in this article a translation from Quantified Boolean Formulae to Answer Set Programming. The computation of a solution of a Quantified Boolean Formula is then equivalent to the computation of a stable model for a normal logic program. The case of unquantified Boolean formulae is also considered since it is equivalent to the case of Quantified Boolean Formulae with only existential quantifiers