Weak integrability breaking: chaos with integrability signature in coherent diffusion

Abstract

We study how perturbations affect dynamics of integrable many-body quantum systems, causing transition from integrability to chaos. Looking at spin transport in the Heisenberg chain with impurities we find that in the thermodynamic limit transport gets diffusive already at an infinitesimal perturbation. Small extensive perturbations therefore cause an immediate transition from integrability to chaos. Nevertheless, there is a remnant of integrability encoded in the dependence of the diffusion constant on the impurity density, namely, at small densities it is proportional to the square root of the inverse density, instead of to the inverse density as would follow from Matthiessen's rule. We show that Matthiessen's rule has to be modified in non-ballistic systems. Results also highlight a nontrivial role of interacting scattering on a single impurity, and that there is a regime where adding more impurities can actually increase transport.

9 pages; v2: 10 pages

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• Non-equilibrium boundary driven quantum systems: models, methods and properties
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• Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains
• Absence of superdiffusion in the quasiperiodic spin chain at weak integrability breaking
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
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• Dephasing enhanced transport in boundary-driven quasiperiodic chains
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