Weak Integrability Breaking: Chaos with Integrability Signature in Coherent Diffusion

Marko Žnidarič
Phys. Rev. Lett. 125, 180605 – Published 28 October 2020
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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 nonballistic 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.

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  • Received 23 June 2020
  • Accepted 5 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.180605

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNonlinear DynamicsCondensed Matter, Materials & Applied PhysicsGeneral Physics

Authors & Affiliations

Marko Žnidarič

  • Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia

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Issue

Vol. 125, Iss. 18 — 30 October 2020

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