Transport in almost integrable models: perturbed Heisenberg chains.

Area of Science:

• Condensed matter physics
• Quantum magnetism
• Statistical mechanics

Background:

• Integrable models, such as the Heisenberg model, possess conservation laws leading to infinite heat conductivity (kappa(T)) at finite temperatures.
• Perturbations to integrable systems typically result in finite, albeit large, transport coefficients.

Purpose of the Study:

• To investigate the impact of different perturbations on the heat conductivity of integrable models.
• To analyze the behavior of kappa(T) under interchain coupling and next-nearest-neighbor interactions.
• To identify the underlying mechanisms responsible for enhanced heat transport.

Main Methods:

• Perturbative calculations using exact diagonalization.
• Moment expansion techniques.
• Analysis of conservation laws in perturbed Heisenberg chains.

Main Results:

• Two classes of perturbations were identified: interchain coupling (J(perpendicular)) and next-nearest-neighbor interaction (J').
• Interchain coupling leads to kappa(T) proportional to 1/J(perpendicular)2, consistent with golden-rule arguments.
• Next-nearest-neighbor interaction results in a significantly larger kappa(T) proportional to 1/J'4, indicating a different transport mechanism.

Conclusions:

• A new approximate conservation law in the J-J' Heisenberg chain explains the enhanced heat conductivity observed for next-nearest-neighbor interactions.
• This finding highlights the importance of subtle conservation laws in determining transport properties in quantum systems.
• The study provides insights into the breakdown of integrability and its effect on thermal transport.