Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems

TL;DR

This paper introduces a two-dimensional quasiperiodic model exhibiting a multifractal critical phase, analyzes its phase diagram and transport properties, and discusses potential realization in superconducting circuits, expanding understanding of MCP in higher dimensions.

Contribution

It presents the first 2D quasiperiodic model with a multifractal critical phase and explores its phase diagram, transport behavior, and experimental realization possibilities.

Findings

Identification of a 2D multifractal critical phase

Phase diagram mapping of the 2D quasiperiodic system

Analysis of wave packet diffusion and transport properties

Abstract

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.