Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories

Area of Science:

• Quantum Information Dynamics
• Condensed Matter Physics
• Quantum Field Theory

Background:

• The Lieb-Robinson bound sets limits on quantum information propagation in many-body systems.
• The butterfly effect describes the rapid spread of local perturbations in chaotic quantum systems.
• Understanding these dynamics is crucial for probing fundamental quantum behavior.

Purpose of the Study:

• To explore the relationship between the Lieb-Robinson bound and the butterfly effect.
• To investigate the butterfly velocity (vB) as a state-dependent effective Lieb-Robinson velocity.
• To analyze the role of strong coupling on butterfly velocity using holographic methods.

Main Methods:

• Holographic techniques were employed to study butterfly velocity in diverse quantum field theories.
• Comparisons were made with free-particle computations to highlight the effects of strong coupling.
• The behavior of butterfly velocity was analyzed across different temperature regimes.

Main Results:

• The butterfly velocity (vB) was identified as a state-dependent effective Lieb-Robinson velocity.
• In strongly coupled quantum field theories, vB was found to be constant or decrease as temperature lowers.
• The study provides insights into the interplay between quantum chaos and information propagation bounds.

Conclusions:

• The butterfly velocity offers a more nuanced, state-dependent perspective on quantum information propagation limits.
• Strong coupling and temperature significantly influence the dynamics of quantum information spread.
• The findings have implications for understanding quantum chaos and experimental quantum information science.