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arXiv:2006.13891 · Physical review. B./Physical review. B

Ballistic-to-diffusive transition in spin chains with broken integrability

João S. Ferreira, Michele Filippone

Published Nov 9, 2020• 18 citations
arXivHTMLPDF

Abstract

We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin chain. Studying the evolution of the spin current density ${\mathcal{J}}^{s}$ as a function of the system size $L$, we show that, accounting for boundary effects, the transition has a nontrivial universal behavior close to the XX limit. It is controlled by the scattering length ${L}^{*}\ensuremath{\propto}{V}^{\ensuremath{-}2}$, where $V$ is the strength of the integrability-breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient ``quasiballistic'' regime at length scales much shorter than ${L}^{*}$. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on matrix product operator numerical simulations and agree with perturbative analytical calculations.

DOI
10.1103/physrevb.102.184304

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We study an open Heisenberg XXZ spin chain with long-range Ising-type interaction, which is incoherently driven at its boundaries and, therefore, a far-from-equilibrium steady-state current is induced. Quantum Monte Carlo techniques make a regime accessible where the system size is large enough to examine the transition from a diffusive to a ballistic transport regime. We find that the chain lengths for this transition are increasing with decreasing range of the Ising-type interactions between distant spins, whereas the strength of the incoherent driving does not have a relevant effect on the transport transition. The transition can be explained by the suppression of ferromagnetic domains at the edges of the chain.
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The anomalous spin diffusion of the integrable easy-axis Heisenberg chain originates in the ballistic transport of symmetry sectors with nonzero magnetization. Ballistic transport is replaced by normal dissipative transport in all magnetization sectors upon introducing the integrability-breaking perturbations, including external driving. Such behavior implies that the diffusion constant obtained for the integrable model is relevant for the spread of spin excitations but not for the spin conductivity. We present numerical results for closed systems and driven open systems, indicating that the diffusion constant shows a discontinuous variation as the function of perturbation strength.