Master Thesis
Relevance of electronic interactions at quasiperiodicity-driven localization transitions
Mariana Gil Guerra de Almeida Abreu
In real materials, disorder can induce (Anderson) insulating phases. Notably, quasiperiodic modulations can also strongly affect wavefunction localization. As the quasiperiodic potential increases, single-particle states transition from delocalized to critical and finally to localized, with metal-insulator transitions distinct from those in disordered systems.
The simplest model capturing this transition is the Aubry-André model, which features a remarkable duality between localized and delocalized states, recently shown to be a generic feature, but somehow hidden, near the transition.
Recently, studies in quasiperiodicity were extended to 1D systems of interacting spinless fermions. Interestingly, such interactions were found to become irrelevant around the transition, with eigenstates following the hidden-duality scenario of the non-interacting limit.
This project explores the effects of spinful interactions in quasiperiodicity-driven localization transitions, specifically, whether they become relevant, as in higher-dimensional disorder-driven transitions, or remain irrelevant, as in the spinless case. We aim to determine whether these transitions can always be described by a non-interacting theory or if spinful interactions alter their nature.
To study the system's ground-state properties, we employ the Density Matrix Renormalization Group (DMRG), which determines many-body quantum states with polynomial complexity in system size.
Our results show that spinful interactions are relevant, modifying the nature and critical properties of the quasiperiodicity-driven localization transition. Unlike the spinless case, excitations at criticality display interacting behavior.
Additionally, we investigate the interaction-driven ordered transition in the spinless model. This analysis revealed a highly interacting critical point. Within the LL phase, the single-particle observable (OIPR) and the Luttinger parameter capture information of the same nature.