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arXiv · 2012.09853

In search of a many-body mobility edge with matrix product states in a Generalized Aubry-Andr\'e model with interactions

Nicholas Pomata·Sriram Ganeshan·Tzu-Chieh Wei
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Abstract

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. To search for a many-body mobility edge in the interacting case, we exploit the advantages of SIMPS that it targets many-body states in an energy-resolved fashion and does not require all many-body states to be localized for some to converge. 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. We benchmark the algorithm's output both for parameters that give fully converged, `MBL-like' localized states and for delocalized parameters where SIMPS fails to converge. In the intermediate cases, where the parameters produce a single-particle mobility edge, we find many-body states that develop entropy oscillations as a function of cut position at larger bond dimensions. These oscillations at larger bond dimensions, which are also found in the fully-localized benchmark but not the fully-delocalized benchmark, occur both at the band edge and center and may indicate convergence to a non-thermal state (either localized or critical).

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Nicholas Pomata, Sriram Ganeshan, Tzu-Chieh Wei. 2020-12-17. In search of a many-body mobility edge with matrix product states in a Generalized Aubry-Andr\'e model with interactions. https://arxiv.org/abs/2012.09853

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