Universal Defects Statistics with Strong Long-Range Interactions

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Physics
• Quantum Phase Transitions

Background:

• Quasi-static transformations (slow quenches) of quantum systems across quantum critical points typically generate topological defects.
• The Kibble-Zurek mechanism explains defect formation in local quantum systems via a classical combinatorial process.
• Long-range interactions are known to disrupt conventional Kibble-Zurek scaling, leading to a defect density independent of transformation rate.

Purpose of the Study:

• To analytically determine the full counting statistics of defects generated by slow annealing in a strong long-range quantum system across its quantum critical point.
• To investigate the nature of defect generation mechanisms in systems with long-range interactions.
• To explore the universality of defect statistics beyond simple density in such systems.

Main Methods:

• Analytical determination of defect statistics.
• Focus on systems with strong long-range interactions undergoing slow annealing across a quantum critical point.
• Investigation of the full counting statistics, not just defect density.

Main Results:

• The mechanism of defect generation in long-range systems is identified as a purely quantum process with no classical analogue.
• Universality is observed not only in the defect density but also in all moments of the defect distribution.
• The defect density is independent of the transformation rate, consistent with previous predictions for long-range systems.

Conclusions:

• The study reveals a novel, purely quantum mechanism for topological defect generation in many-body systems with long-range interactions.
• Universality in defect statistics, encompassing all moments, is a key feature of these quantum processes.
• The findings offer testable predictions for experimental platforms like Rydberg gases and trapped ions.