Conductivity in the Heisenberg chain with next-to-nearest-neighbor interaction

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• The XXZ model is a fundamental model in quantum magnetism, known for its exact integrability.
• Perturbations can break integrability, altering the system's properties and requiring advanced analytical techniques.
• Understanding metallic behavior in quantum systems is crucial for materials science and technological applications.

Purpose of the Study:

• To rigorously prove ideal metallic behavior (infinite conductivity) in a spin chain with a specific perturbation.
• To establish strict lower bounds on the zero-temperature Drude weight.
• To investigate the role of integrability-breaking terms on the system's conductivity and Drude weight relations.

Main Methods:

• Utilizing exact renormalization group (RG) methods.
• Proving the convergence of RG expansions.
• Analyzing the impact of irrelevant terms that preserve lattice symmetries.

Main Results:

• Demonstrated strictly positive lower bounds for the zero-temperature Drude weight, indicating infinite conductivity.
• Established that the system exhibits ideal metallic behavior despite the integrability-breaking perturbation.
• Showed that the Drude weight satisfies parameter-free relations consistent with the unperturbed system.

Conclusions:

• The perturbed XXZ spin chain maintains ideal metallic properties, characterized by infinite conductivity.
• Exact renormalization group methods are effective in analyzing systems with broken integrability.
• The findings have implications for understanding transport properties in quantum materials.