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Gaussian-state approaches to quantum spin systems away from equilibrium

Abstract : What happens when a quantum many-body system is brutally driven away fromequilibrium ? Toward which kind of states does it relax and what informationcan one extract from the resulting dynamics ? Providing answers to these questionsis a challenging problem that spured the interest of a whole community ofphysicists. However, the numerical cost required to investigate the behaviour ofthese systems, particularly for large system sizes, motivated the development ofcutting-edge numerical and theoretical techniques.This thesis aims at contributing to these efforts by proposing a set of methodsbased on a representation of the systems in terms of a Gaussian field theory, withthe purpose of studying the evolution of spin systems. More specifically, thesemethods are applied to several models inspired by cold-atoms experiments simulatingthe behaviour of spin systems, with a stress on the study of localizationphenomena. Therefore, this thesis highlights the emergence of localization in systemsdevoid of disorder due to an interference effect, the so-called Aharonov-Bohmcaging; as well as a geometrically disordered quantum Ising model displaying adynamics exploring a rich spectrum ranging from balistic diffusion to anomalousdiffusion, an then localization - this last example offers a scenario richer than theone exhibited by the dynamics of free particles in a disordered medium. Finally,we explored the possibility for Gaussian approaches to describe the dynamics ofinteracting systems and their relaxation toward thermal states.
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Submitted on : Wednesday, January 6, 2021 - 9:49:21 AM
Last modification on : Thursday, January 7, 2021 - 3:29:07 AM
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  • HAL Id : tel-03099280, version 1


Raphaël Menu. Gaussian-state approaches to quantum spin systems away from equilibrium. Condensed Matter [cond-mat]. Université de Lyon, 2020. English. ⟨NNT : 2020LYSEN036⟩. ⟨tel-03099280⟩



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