Abstract

In the context of quantum transport, the XXZ (or anisotropic Heisenberg) chain is a paradigmatic
many-body model, featuring wide spectrum of spin transport behaviour at finite temperature.
Although the unperturbed model is analytically solvable, understanding the effects of even weak
integrability-breaking perturbations (IBP) remains an open problem. The primary aim of this talk is
to highlight the effects of IBP on the spin transport i) in the easy-axis regime and ii) at the isotropic
point of the XXZ chain. In particular, I will show that the anomalous (dissipationless) spin diffusion
of the integrable easy-axis XXZ chain is replaced by a normal spin diffusion upon the addition of
perturbation. Such a fundamental change in the nature of diffusion is reflected via discontinuous
variation of the dc diffusion constant as a function of the perturbation. Next, the impact of the
symmetry of IBP on the spin superdiffusion at the isotropic point of integrable XXZ chain will be
addressed. In this context, our study unveils several remarkable properties: i) the effects of IBP
preserving spin isotropy being qualitatively different from anisotropic IBP, ii) isotropic IBP leads to
a pronounced maximum of the diffusion constant at the isotropic point as the function of spin
anisotropy, and iii) robustness of superdiffusion on finite systems even at appreciable perturbation
strengths.