Conservation laws, integrability and transport in one-dimensional quantum systems

TL;DR

This paper investigates transport phenomena in one-dimensional integrable quantum systems, revealing how certain currents are dominated by diffusion due to lack of overlap with conserved quantities, with implications for experimental measurements.

Contribution

It demonstrates that in specific integrable models, transport is diffusive at finite temperatures because the current operator does not overlap with local conserved quantities, and explores the special case of the Haldane-Shastry model.

Findings

Transport is dominated by diffusion when current operators are orthogonal to conserved quantities.

The Drude weight can be small or zero in these cases, indicating suppressed ballistic transport.

The results relate to experimental observations in spin chain compounds.

Abstract

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where the current operator is also orthogonal to the set of conserved quantities associated with integrability but becomes itself conserved in the thermodynamic limit.