New anomalous Lieb-Robinson bounds in quasiperiodic XY chains

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory
• Statistical Mechanics

Background:

• The Lieb-Robinson (LR) bound governs the speed of quantum information propagation in many-body systems.
• Standard LR bounds imply ballistic transport, where correlations spread linearly with time.
• Anomalous transport phenomena challenge these standard bounds, suggesting slower propagation.

Purpose of the Study:

• To rigorously prove a new type of anomalous (sub-ballistic) Lieb-Robinson bound.
• To investigate quantum transport in an isotropic XY chain subjected to a quasiperiodic transversal magnetic field.
• To explore anomalous LR bounds with power-law tails in a random dimer field.

Main Methods:

• Rigorous mathematical proof techniques.
• Analysis of one-body Schrödinger operators and their transport exponents.
• Development of anomalous quantum many-body transport theory.

Main Results:

• A novel anomalous Lieb-Robinson bound of the form |x|≤v|t|^α, with 0<α<1, was derived.
• The exponent α was precisely characterized by the upper transport exponent of a one-body Schrödinger operator.
• This marks the first rigorous derivation of anomalous quantum many-body transport.

Conclusions:

• The study establishes a new paradigm for quantum information propagation, demonstrating sub-ballistic behavior.
• The findings have implications for understanding transport phenomena in complex quantum systems.
• Anomalous LR bounds with power-law tails were also discussed for disordered systems.