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Information Flow and Local Observables in Many Body Localized Systems / Informationsflöden och lokala observabler i mångpartikellokaliserade systemNiemi, Daniel January 2022 (has links)
Disordered quantum many-body systems exhibiting the many-body localization (MBL) phenomenon evade the fate of thermalization due to the existence of an extensively large set of quasi-local integrals of motion (l-bits). Due to the size of the Hilbert space of many-body systems, it is hard to compute the time evolution of many-body systems generally, which hinders our understanding of the MBL phenomenon. Recently it has been proposed in Ref. [1] to time evolve local density matrices of lattice system with short-range interactions using the Petz recovery map. By time evolving local density matrices, information encoded in long-range entanglement that is irrelevant to the time-evolution of local observables is discarded. This method is promising for MBL-systems, primarily because it can be implemented to conserve local constants of the motion. For the case of a MBL system, this means that the l-bits can be (approximately) conserved. This thesis employs the Petz recovery map to time evolve local density matrices of localized 1D lattice systems, modeled by the Aubry-André Hamiltonian. The accuracy of the method is evaluated and the results are used to study the flow of information between subsystems. It is found that the method can accurately time evolve localized density matrices for an Anderson localized system to arbitrary times. For interacting systems, it is shown that the method is accurate for long time if the system is sufficiently localized. Furthermore, the solutions for the local density matrices exhibit the information spread behavior that is predicted by the l-bit theory of the many-body localized phase: both the logarithmic ”light” cone of entanglement and the dephasing dynamics are observed. This work shows that time evolution of local density matrices is a promising method in the pursuit of a better understanding of the nature of localized systems. / I oordnade kvantmekansika mångpartikelsystem förekommer en lokaliserad fas (MBL). System i denna fas undkommer termalisering då det existerar ett extensivt antal kvasi-lokala rörelsekonstanter (l-bitar). Som en följd av Hilbert-rummets storlek för mångpartikelsystem är det svårt att tidsutveckla mångpartikeltillstånd i allmänhet, vilket gör det svårt att undersöka MBL-fenomenet. Det har nyligen föreslagits i Ref. [1] att tidsutveckla lokala täthetsmatriser för växelverkande endimensionella gittersystem med hjälp av Petzs återställningsfunktion. Genom att tidsutveckla lokala täthetsmatriser förkastas information som inte är relevant för lokala observabler. Metoden är lovande för MBL-system då den kan implementeras så att lokala rörelsekonstanter konserveras. Detta innebär för MBL-system att l-bitarna kan konserveras approximativt. I detta arbete används Petzs återställningsfunktion för att tidsutveckla lokala täthetsmatriser i lokaliserade endimensionella gittersystem. Metodens nogrannhet utvärderas och de resulterande tidsserierna används för att studera informationsspridning mellan delsystem. Arbetet visar att Andersonlokaliserade system kan tidsutvecklas med god nogrannhet till godtyckligt långa tider. Vidare visas att metoden nogrannt kan tidsutveckla MBL-system till långa tider, givet att lokaliseringslängden är kort nog. Slutligen används metoden för att studera informationsflödet mellan delsystem, och resultaten återskapar det beteende som väntas från den fenomenologiska l-bitteorin: informationen sprids logaritmiskt över tid och avfasningsdynamik observeras. Arbetet visar att den föreslagna metoden är lovande i jakten på en utökad förståelse av MBL-system.
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Collective localization transitions in interacting disordered and quasiperiodic Bose superfluids / Transitions de localisation collective dans les superfluides de Bose désordonnés ou quasipériodiquesLellouch, Samuel 12 December 2014 (has links)
Ce mémoire présente une étude théorique des propriétés de localisation collective dans les superfluides de Bose désordonnés ou quasipériodiques. S'il est connu depuis Anderson que le désordre peut localiser les particules libres, comprendre ses effets dans les systèmes quantiques en interaction, où il est à l'origine de transitions de phase et d'effets de localisation non-Triviaux, représente aujourd'hui un défi majeur. En nous focalisant sur le cas d'un gaz de Bose dans le régime de faibles interactions, bien décrit par la théorie de Bogoliubov, nous étudions les transitions de localisation de ses excitations collectives dans différents contextes. Dans le cas d'un vrai désordre dans l'espace continu tout d'abord, nous développons un formalisme de désordre fort allant au-Delà des études antérieures, aboutissant à une description complète des propriétés de localisation des excitations en dimension arbitraire. Nous présentons un diagramme de localisation générique, et une interprétation microscopique de la propagation des excitations dans le désordre. Dans un second temps, nous considérons le cas d'un potentiel quasipériodique unidimensionel, aux propriétés intermédiaires entre un vrai désordre et un potentiel périodique. Notre traitement analytique et numérique du problème révèle une transition de localisation collective, que nous caractérisons et interprétons en termes de localisation dans un potentiel effectif multiharmonique. Pour finir, nous considérons le cas d'un gaz de Bose à deux composants. Nous développons le formalisme général pour étudier ces questions et décrivons la physique de base de ces systèmes qui présentent leurs propres spécificités. / In this thesis, we theoretically investigate the collective localization properties of weakly-Interacting Bose superfluids subjected to disordered or quasiperiodic potentials. While disorder has been recognized since Anderson to induce single-Particle localization, the interplay between disorder and interactions in quantum systems is today among the most challenging questions in the field, and underlies fascinating phase transitions and non-Trivial localization effetcs. Focusing on Bose gases in the weakly-Interacting regime for which the Bogoliubov theory proves a successful tool, we study the localization transitions of collective excitations in several contexts. First, in the case of a continuous true disorder, we develop a strong-Disorder formalism going beyond previous studies, providing us with a complete description of the localization behaviour of collective excitations in arbitrary dimension. A generic localization diagram is obtained and the transport of excitations in the disorder is microscopically interpreted. Secondly, we consider the case of one-Dimensional quasiperiodic potentials, which are known to display intermediate properties between periodic and disordered ones. We perform a numerical and analytical treatment of the localization problem of collective excitations, allowing us to quantitatively characterize and interpret the localization transition in terms of an effective multiharmonic problem. Finally, we set up the general inhomogeneous formalism to address such issues in multicomponent Bose gases, and enlighten the basic physic of such systems, which are known to exhibit their own specific features.
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