Orthogonality Catastrophe in Dissipative Quantum Many-Body Systems

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Physics
• Open Quantum Systems

Background:

• Orthogonality catastrophe describes the loss of overlap between initial and final states in quantum systems after a perturbation.
• Local dissipation introduces environmental interactions, leading to decoherence and state evolution.
• Understanding these phenomena is crucial for quantum information processing and condensed matter theory.

Purpose of the Study:

• To investigate an analog of orthogonality catastrophe in quantum many-body systems subjected to local dissipative impurities.
• To analyze the fidelity's time evolution and its scaling behavior under dissipation.
• To explore the interplay between long-range correlations, dissipation, and decoherence.

Main Methods:

• Development of a second-order cumulant expansion for Liouvillian dynamics.
• Analytical derivation of the fidelity's universal scaling form F(t)∝t^{θ}e^{-γt}.
• Application and substantiation of the theoretical framework to specific models.

Main Results:

• A universal fidelity scaling F(t)∝t^{θ}e^{-γt} was identified in systems with long-range correlations under local dissipation.
• The exponential decay rate γ signifies environmental decoherence, critically slowed by an algebraic fidelity contribution.
• The phenomenon was demonstrated in the 1D transverse field quantum Ising model, XY and XX spin chains, and 2D Bose gas.

Conclusions:

• Local dissipative impurities can induce an analog of orthogonality catastrophe in quantum many-body systems.
• This effect leads to a universal fidelity scaling that combines algebraic and exponential decay.
• Local dissipation offers a potential route to probe real-time correlations and delay decoherence in open quantum systems.