We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin chain. Studying the evolution of the spin current density ${\mathcal{J}}^s$ as a function of the system size $L$, we show that, accounting for boundary effects, the transition has a nontrivial universal behavior close to the XX limit. It is controlled by the scattering length $L^{*}\propto V^{-2}$, where $V$ is the strength of the integrability-breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient “quasiballistic” regime at length scales much shorter than $L^{*}$. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on matrix product operator numerical simulations and agree with perturbative analytical calculations.

• Received 26 June 2020
• Revised 28 September 2020
• Accepted 22 October 2020
• Corrected 11 December 2020

DOI:https://doi.org/10.1103/PhysRevB.102.184304