Stability of Periodically Driven Topological Phases against Disorder

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Physics

Background:

• Time-dependent periodic fields create exotic topological phases of matter.
• These nonequilibrium states show robustness against disorder, similar to equilibrium topological phases.
• Proving the existence of such topological phases generally remains an open problem.

Purpose of the Study:

• To propose a universal effective theory for predicting topological phases in driven systems.
• To analytically determine the existence of topological phases for finite driving frequencies and varying disorder.
• To identify the critical point and critical exponents for the topological-trivial phase transition.

Main Methods:

• Leveraging modern free probability theory.
• Applying concepts from random matrix theory.
• Developing a universal effective theory for driven-disordered systems.

Main Results:

• The theory analytically predicts the existence of topological phases for finite driving frequencies.
• It demonstrates that systems can be topological or trivial depending on disorder strength.
• The theory accurately predicts the critical point and critical exponents for the phase transition.

Conclusions:

• The developed theory provides an analytical framework for understanding topological phases in driven systems.
• The findings show a disorder-induced transition between topological and trivial phases.
• Results are validated against exact diagonalizations of standard models, offering guidance for experimental exploration.