Non-interacting universality of quasiperiodic-induced localization transitions in 1d

We devise a renormalization-group method to analyze the localization properties of interacting and non-interacting [1,2] many-body ground-states in 1d quasiperiodic systems.

The RG flow is generated by increasing the size of commensurate approximants to approach the infinite incommensurate system. Our method tracks how the ground-state energy depends on phase twists and real-space shifts under this flow.

For widely different interacting and non-interacting models, we show that twists (shifts) become irrelevant in the localized (extended) phase. We exploit these effects to determine many-body delocalization-localization critical points with unprecedented accuracy and to perform thorough scaling analysis around criticality.

Remarkably, our findings show that close to delocalization critical points interactions are irrelevant and the many-body ground-state flows to non-interacting fixed points, i.e. the ground-state physics close to criticality is not affected by interactions.

[1] Hidden dualities in 1D quasiperiodic lattice models, Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro, SciPost Phys. 13, 046 (2022)

[2] Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants, Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro, arXiv:2206.13549 (2022)