Many-body localization in quasiperiodic systems

Abstract

Many-body localization (MBL) is a phenomenon in which an isolated many-body quantum system fails to reach thermal equilibrium, with information in the initial condition remaining localized indefinitely. Although MBL has been most widely studied in systems with random disorder, the same phenomenon also occurs in quasiperiodic systems, which are deterministic. Interestingly, some quasiperiodic systems show richer behaviors than just either fully MBL or fully thermalized. In particular, there is a regime that is non-ergodic but has extended states, and a regime whose single-particle orbitals are critical between being extended and localized. The nature and consequences of such phenomena in interacting thermodynamic systems are not yet fully understood. Another important distinction from random MBL is the lack of rare low-disorder regions. On an infinitely long random chain, there exist regions that accidentally have low disorder and may act as thermal seeds to thermalize the entire chain. Although there is no such low-disorder region in quasiperiodic systems, it is not known whether other types of rare regions exist that may destabilize thermodynamic MBL.

In this dissertation, we study these problems both numerically and analytically. First, we develop numerical probes for the non-ergodic extended regime and explain its origin as a finite-time phenomenon. Second, we study the consequences of approximate mirror centers in the potential, which is one of the mechanisms for single-particle critical orbitals, on interacting many-body systems. Based on these mirror-induced structural resonances, we then construct an asymptotically solvable model for many-body critical phases, showing features such as thermodynamic many-body mobility edges, scars, and inverted scars. Finally, we study the possibility that quasiperiodic MBL is destabilized by rare regions originating from such structural resonances.