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Diffusion and ballistic transport in one-dimensional quantum systems.

J Sirker¹, R G Pereira, I Affleck

¹Department of Physics and Research Center OPTIMAS, TU Kaiserslautern, D-67663 Kaiserslautern, Germany.

Physical Review Letters

|April 7, 2010

Summary

This summary is machine-generated.

Diffusion is universally present in one-dimensional (1D) interacting systems with periodic potentials, contrary to prior conjectures of ballistic transport. This study explains experimental observations and provides a parameter-free formula for spin-lattice relaxation rates.

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Area of Science:

Condensed Matter Physics
Quantum Mechanics
Statistical Mechanics

Background:

One-dimensional (1D) systems are theoretically predicted to exhibit ballistic transport.
Experimental observations in the S=1/2 1D Heisenberg model show a large diffusive response, which contradicts theoretical predictions.
This discrepancy has remained unexplained, posing a puzzle in condensed matter physics.

Purpose of the Study:

To investigate the transport properties of interacting 1D systems subjected to a periodic lattice potential.
To reconcile the theoretical prediction of ballistic transport with experimental observations of diffusion.
To develop a theoretical framework explaining the observed diffusive behavior.

Main Methods:

Theoretical analysis of interacting 1D systems with periodic lattice potentials.
Development of a parameter-free formula for the spin-lattice relaxation rate.
Utilizing a time-dependent density matrix renormalization group (TD-DMRG) algorithm.
Direct calculation of current decay in the thermodynamic limit.

Main Results:

Demonstrated that diffusion is a universal phenomenon in interacting 1D systems with periodic potentials.
Presented a parameter-free formula for the spin-lattice relaxation rate that shows excellent agreement with experimental data.
Calculated current decay, revealing an anomalously large time scale even at high temperatures.

Conclusions:

The study overturns the conjecture that transport in integrable 1D systems is necessarily ballistic.
Diffusion is shown to be universally present in interacting 1D systems with periodic potentials.
The findings provide a theoretical explanation for experimental results and offer a new understanding of transport in such systems.