Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems

The multifractal critical phase (MCP) fundamentally differs from extended and localized phases, exhibiting delocalized distributions in both position and momentum spaces. The investigation on the MCP has largely focused on one-dimensional quasiperiodic systems. Here, we introduce a two-dimensional (2D) quasiperiodic model with a MCP. We present its phase diagram and investigate the characteristics of the 2D system's MCP in terms of wave packet diffusion and transport based on this model. We further investigate the movement of the phase boundary induced by the introduction of next-nearest-neighbor hopping by calculating the fidelity susceptibility. Finally, we consider how to realize our studied model in superconducting circuits. Our work opens the door to exploring MCP in 2D systems.