Determination of the Nonequilibrium Steady State Emerging from a Defect

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Statistical Mechanics

Background:

• Understanding nonequilibrium quantum systems is crucial for fields like quantum computing.
• Localized defects can significantly alter system dynamics.
• Characterizing emergent phenomena in quantum many-body systems remains a challenge.

Purpose of the Study:

• To investigate the nonequilibrium time evolution of quantum states with localized defects.
• To identify and characterize the emergence of light cones in such systems.
• To develop a general procedure for describing late-time dynamics and quasi-stationary states.

Main Methods:

• Analysis of time evolution under a Hamiltonian with a localized defect.
• Identification of light cone propagation separating distinct macroscopic regions.
• Development of a method to obtain quasi-stationary states for local observables.
• Exact solution of the transverse-field Ising chain with a specific defect (boundary condition quench).

Main Results:

• A light cone is identified, separating the system into regions with different macroscopic properties.
• A general procedure is proposed to obtain quasi-stationary states for late-time dynamics.
• The proposed method is validated by exactly solving the transverse-field Ising chain with a defect.

Conclusions:

• Localized defects can lead to the formation of light cones and distinct macroscopic regions.
• The developed procedure effectively describes the late-time dynamics of local observables.
• The study provides a framework for understanding complex quantum dynamics in the presence of defects.