Diffusion and ballistic transport in one-dimensional quantum systems

Abstract

It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling and has not been explained so far. Here, we show that, contrary to common belief, diffusion is universally present in interacting 1D systems subject to a periodic lattice potential. We present a parameter-free formula for the spin-lattice relaxation rate which is in excellent agreement with experiment. Furthermore, we calculate the current decay directly in the thermodynamic limit using a time-dependent density matrix renormalization group algorithm and show that an anomalously large time scale exists even at high temperatures.

4 pages, published version

References in corpus (4)

• Spin conductivity in almost integrable spin chains
• Real-time dynamics at finite temperature by DMRG: A path-integral approach
• Spin diffusion and the anisotropic spin-1/2 Heisenberg chain
• Finite Drude weight for 1D low temperature conductors

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