In search of a many-body mobility edge with matrix product states in a Generalized Aubry-André model with interactions

Nicholas Pomata, Sriram Ganeshan, Tzu-Chieh Wei

Published 2020-12-17Version 1

We investigate the possibility of a many-body mobility edge in the Generalized Aubry-Andr\'e (GAA) model with interactions using the Shift-Invert Matrix Product States (SIMPS) algorithm (Phys. Rev. Lett. 118, 017201 (2017)). The non-interacting GAA model is a one-dimensional quasiperiodic model with a self-duality induced mobility edge. The advantage of SIMPS is that it targets many-body states in an energy-resolved fashion and does not require all many-body states to be localized for convergence, which allows us to test if the interacting GAA model manifests a many-body mobility edge. Our analysis indicates that the targeted states in the presence of the single particle mobility edge match neither `MBL-like' fully-converged localized states nor the fully delocalized case where SIMPS fails to converge. An entanglement-scaling analysis as a function of the finite bond dimension indicates that the many-body states in the vicinity of a single-particle mobility edge behave closer to how delocalized states manifest within the SIMPS method.