Microscopic Origin of Ideal Conductivity in Integrable Quantum Models

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Statistical Mechanics

Background:

• Nonergodic dynamical systems exhibit anomalous transport, notably diverging DC conductivities in integrable quantum systems.
• Understanding the microscopic origins of these transport properties, especially ideal conductivity, remains a key challenge.
• The nature of spin and charge Drude weights in systems lacking chemical potentials has been a long-standing controversy.

Purpose of the Study:

• To elucidate the microscopic origin of ideal conductivity in nonergodic systems.
• To rigorously resolve the controversy surrounding spin and charge Drude weights.
• To develop an efficient computational method for calculating exact Drude weights.

Main Methods:

• Utilizing group-theoretic arguments to analyze thermodynamic particle content.
• Employing a hydrodynamic description for calculating Drude weights.
• Simulating stationary currents from inhomogeneous quenches in bipartitioned initial states.

Main Results:

• The study explains the microscopic origin of ideal conductivity through thermodynamic particle content.
• It rigorously resolves the controversy regarding spin and charge Drude weights in the absence of chemical potentials.
• A novel, efficient computational method for exact Drude weight calculation is presented.

Conclusions:

• The developed hydrodynamic method allows calculation of exact Drude weights, applicable to systems like the anisotropic Heisenberg model.
• The research provides a definitive resolution to the debate on spin and charge Drude weights.
• Remarkably, the spin Drude weight and asymptotic spin current rates show a discontinuous, fractal dependence on the anisotropy parameter.