Many-body localization in two-dimensional quasiperiodic systems

Systems that fail to thermalize over a long period of time are essential for both practical applications and fundamental science.

For the former, such systems can serve as stable platforms for many future technologies that operate at the quantum level, such as information storage and quantum computing devices.

For the latter, such systems can host exotic quantum phases of matter by suppressing thermal excitations that tend to destroy the order. One of the most famous classes of systems that resist thermalization is the class of many-body localized (MBL) systems.

Until now, it has been confirmed both experimentally and theoretically that the MBL can exist in isolated one-dimensional systems, either random or quasiperiodic ones. In higher dimensions, the fate of MBL is still unclear.

A famous avalanche theory predicts the instability of the MBL phase in higher dimensional random systems due to the rare regions of weak disorder. However, quasiperiodic systems do not contain rare regions, which might stabilize the higher-dimensional MBL. The main objective of this proposal is to investigate MBL in two-dimensional quasiperiodic systems.

The goal is to show whether MBL in quasiperiodic systems can survive in dimensions higher than one.

With a novel numerical approach, which will allow me to study the dynamics of large systems (~100 sites) and reach long times (several hundred hopping times), combined with analytical calculations, I plan to investigate the microscopic mechanisms behind the stability/instability of the MBL phase in two-dimensional quasiperiodic models.

My research will (i) provide an insight into the interplay between interactions and quasiperiodicity in two dimensions, (ii) produce a new interesting range of localization phenomena, and (iii) present a highly tunable and experimentally accessible setting where slow dynamics and localization can be studied, and possibly exploited for technological applications.