In search of a many-body mobility edge in a quasiperiodic system with matrix product states

Speaker: Nikko Pomata, Stonybrook

When: December 23, 2020 (Wed), 12:00PM to 01:00PM (add to my calendar)

This event is part of the Biophysics/Condensed Matter Seminar Series.

I will be discussing my recent work arXiv:2012.09853 with Sriram Ganeshan and Tzu-Chieh Wei, in which we investigated the possibility of a many-body mobility edge in an interacting generalized Aubry-André (GAA) model using Yu, Pekker, & Clark's Shift-Invert Matrix Product States (SIMPS) eigenstate extraction method. In the single-particle spectrum, this one-dimensional quasiperiodic model has a self-duality-induced mobility edge. We have used the energy-targeting SIMPS method to extract candidate eigenstates on either side of a hypothetical many-particle mobility edge. Our primary problem once we have extracted these eigenstates, which will be the focus of my talk, is determining which of these candidate eigenstates is a good approximation of a true eigenstate. I will discuss the various metrics we have used to try to differentiate between such "good" and "bad" candidates, from energy error and entropy scaling to Uhlmann fidelities. These methods have allowed us to reach tentative conclusions that several of the regions studied behave in a generally delocalized manner, while leaving open the possibility of a mobility edge at one of the parameters under consideration. I will conclude by exploring the ways we may extend our analysis to add rigor to our conclusions.

Join on zoom: https://bostonu.zoom.us/j/97175119145?pwd=N1c1SkVYT0x1RjJJbGFsVTIxdzJYQT09