Finite-temperature spin transport in integrable isotropic spin chains (i.e., spin chains with continuous non-Abelian symmetries) is known to be superdiffusive, with anomalous transport properties displaying remarkable robustness to isotropic integrability-breaking perturbations. Using a discrete-time classical model, we numerically study the crossover to conventional diffusion resulting from both noisy and Floquet isotropic perturbations of strength $\ensuremath{\lambda}$. We identify an anomalously-long crossover timescale ${t}_{★}\ensuremath{\sim}{\ensuremath{\lambda}}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}6$ in both cases. We discuss our results in terms of a kinetic theory of transport that characterizes the lifetimes of large solitons responsible for superdiffusion.
Recent studies of quantum many-body dynamics uncover many intriguing phenomena of thermalization and localization in the presence of a quasiperiodic potential. In this paper, the authors study nonequilibrium steady states of the one-dimensional interacting Aubry-Andre-Harper model by taking advantage of tensor network-based algorithms. In a weak potential regime, they find a superdiffusive to subdiffusive transition in spin transport within the thermal phase. The correlation structure of the steady states derived from the quantum mutual information shows an unusual oscillation pattern before reaching the localization transition. Our results suggest a rich phase diagram for the model.
We study high-temperature magnetization transport in a many-body spin-1/2 chain with on-site quasiperiodic potential governed by the Fibonacci rule. In the absence of interactions it is known that the system is critical with the transport described by a continuously varying dynamical exponent (from ballistic to localized) as a function of the on-site potential strength. Upon introducing weak interactions, we find that an anomalous noninteracting dynamical exponent becomes diffusive for any potential strength. This is borne out by a boundary-driven Lindblad dynamics as well as unitary dynamics, with agreeing diffusion constants. This must be contrasted to a random potential where transport is subdiffusive at such small interactions. Mean-field treatment of the dynamics for small
U always slows down the noninteracting dynamics to subdiffusion, and is therefore unable to describe diffusion in an interacting quasiperiodic system. Finally, briefly exploring larger interactions we find a regime of interaction-induced subdiffusive dynamics, despite the on-site potential itself having no ``rare regions.''
There are two well-established ways of characterizing transport properties. The first is via the spread of correlations in an isolated system. The second is through the system-size dependence of the current, when a potential bias is applied by connecting the two ends of the system to reservoirs. These are two different experiments, but usually the result of one experiment can be inferred from that of the other. This work presents a surprising counterexample. The authors show that, at the critical point of the Aubry-Andr\'e-Harper model, transport in the presence of reservoirs is drastically different from transport in the isolated system. The scaling of current with system size shows clear subdiffusive behavior, while the spread of correlations does not show any subdiffusive behavior. It actually hints at superdiffusion. This implies that the understanding of the relation between transport in open and in isolated systems needs to be reexamined.
Superdiffusive transport with dynamical exponent
z=3/2 has been firmly established at finite temperature for a class of integrable systems with a non-abelian global symmetry
G. On the inclusion of integrability-breaking perturbations, diffusive transport with
z=2 is generically expected to hold in the limit of late time. Recent studies of the classical Haldane-Ishimori-Skylanin model have found that perturbations that preserve the global symmetry lead to a much slower timescale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength
λ, the characteristic timescale for diffusion goes as
t∗∼λ−α for some
α. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the canonical quantum model showing superdiffusion: the
S=1/2 quantum Heisenberg chain. We consider a ladder configuration and look at various perturbations that either break or preserve the
SU(2) symmetry, leading to scaling exponents consistent with those observed in one classical study arXiv:2402.18661:
α=2 for symmetry-breaking terms and
α=6 for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with
G=SU(4) and find consistent results. Finally, we consider a generalization to an
SU(3) ladder and find that the
α=6 scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-abelian symmetry
G.
The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization $m\ensuremath{\ne}0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\mathcal{D}}_{0}(\mathrm{\ensuremath{\Delta}})$ on the spin anisotropy $\mathrm{\ensuremath{\Delta}}$, with a pronounced maximum at $\mathrm{\ensuremath{\Delta}}=1$. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at $\mathrm{\ensuremath{\Delta}}=1$ that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.