Localization and critical diffusion of quantum dipoles in two dimensions

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Disordered systems

Background:

• Anderson localization typically describes wave function decay in disordered systems.
• Conventional models often assume short-range interactions, limiting applicability to systems with long-range correlations.

Purpose of the Study:

• Investigate quantum propagation of dipole excitations in two-dimensional systems.
• Analyze the impact of long-range hops on localization phenomena.
• Characterize the behavior of critical wave functions and diffusion constants.

Main Methods:

• Utilized a modified nonlinear supermatrix sigma model.
• Performed a two-loop analysis to study quantum propagation.
• Examined the conditions for critical states and diffusion-to-Levy flight transitions.

Main Results:

• Critical wave functions for dipoles always exist, characterized by a scale-independent diffusion constant.
• In T-invariant systems, states remain critical across all parameter values.
• Non-T-invariant systems can exhibit a metal-insulator transition between ordinary diffusion and Levy flights.

Conclusions:

• The presence of long-range hops fundamentally alters localization dynamics compared to Anderson localization.
• The study reveals distinct diffusion regimes and transitions driven by system symmetries.
• The findings provide insights into quantum transport in complex, disordered environments.