Half-Integer Quantized Topological Response in Quasiperiodically Driven Quantum Systems.

Area of Science:

• Condensed matter physics
• Quantum dynamics
• Topological physics

Background:

• Quantum systems driven by external forces can exhibit exotic phenomena.
• The quantum Hall effect demonstrates quantized charge transport.
• Topological band theory describes robust properties of electronic systems.

Purpose of the Study:

• To investigate energy pumping in a spin system driven by two incommensurate harmonic drives.
• To explore the analogy between this energy pumping and the quantum Hall effect.
• To characterize the topological phase transition and its associated phenomena.

Main Methods:

• Utilizing a spin system driven by two harmonic incommensurate drives.
• Analyzing energy transfer rates and their quantization.
• Investigating the dynamical transition using a synthetic band structure and a Dirac point.
• Applying Kibble-Zurek scaling theory to energy transfer processes.

Main Results:

• Energy is pumped between drives at a quantized average rate, mirroring the quantum Hall effect.
• A nonzero integer pumping rate is observed in the topological regime, while the trivial regime shows no pumping.
• A sharp dynamical transition occurs in the zero-frequency limit, characterized by a Dirac point.
• The pumping rate is quantized to a half-integer at the transition, with universal Kibble-Zurek scaling for energy transfer.

Conclusions:

• The study successfully adapts concepts from quantum phase transitions, quantum information, and topological band theory to understand nonequilibrium dynamics.
• Qubit experiments are identified as a viable platform to observe the universal linear and nonlinear responses of a Dirac point in synthetic dimensions.
• The findings provide a new perspective on quantized energy transfer and topological phenomena in driven quantum systems.