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In the easy-plane regime of XXZ spin chains, spin transport is ballistic, with a Drude weight that has a discontinuous fractal dependence on the value of the anisotropy $Delta = cos pi lambda$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for generic irrational values of $lambda$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $sigma(omega) sim 1/sqrt{omega}$; anomalous response occurs because quasiparticles undergo Levy flights. For rational values of $lambda$, the divergence is cut off at low frequencies and the corrections to ballistic spin transport are diffusive. We also use our approach to recover that at the isotropic point $Delta=1$, spin transport is superdiffusive with $sigma(omega) sim omega^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.
We reveal a continuous dynamical heating transition between a prethermal and an infinite-temperature stage in a clean, chaotic periodically driven classical spin chain. The transition time is a steep exponential function of the drive frequency, showi
In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths with fixed, different magnetization. We take grad
Recently, antiferromagnets have received revived interest due to their significant potential for developing next-generation ultrafast magnetic storage. Here we report dc spin pumping by the acoustic resonant mode in a canted easy-plane antiferromagne
This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical integrable s