Ballistic transport in integrable quantum chains with degenerate spectra

TL;DR

This paper investigates how integrable quantum chains like the XXZ and Hubbard models exhibit abrupt changes in transport properties due to degeneracies in their spectra, especially near the noninteracting limit, revealing new insights into their conserved quantities.

Contribution

It demonstrates the connection between spectral degeneracies and discontinuities in transport stiffnesses, introducing degenerate perturbation methods for large systems and analyzing the nonlocal nature of effective interactions.

Findings

Discontinuous jumps in spin and charge current stiffnesses at high temperatures.

Degeneracies in noninteracting models cause these jumps, explained via degenerate perturbation theory.

Local conserved quantities are insufficient to fully explain the observed transport behavior.

Abstract

We study the ballistic transport in integrable lattice models, i.e., the spin XXZ and Hubbard chains, close to the noninteracting limit. The stiffnesses of spin and charge currents reveal, at high temperatures, a discontinuous reduction (jump) when the interaction is introduced. We show that the jumps are related to the large degeneracy of the parent noninteracting models. These degeneracies are properly captured by the degenerate perturbation calculations which may be performed for large systems. We find that the discontinuities and the quasilocality of the conserved current in this limit can be traced back to the nonlocal character of an effective interaction. From the latter observation we identify a class of observables which show discontinuities in both models. We also argue that the known local conserved quantities are insufficient to explain the stiffnesses in the Hubbard chain in the regime of weak interaction.