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

• URL: http://arxiv.org/abs/2006.13891v3
• Date: Wed, 16 Dec 2020 21:10:16 GMT
• Title: Ballistic-to-diffusive transition in spin chains with broken integrability
• Authors: Jo\~ao S. Ferreira and Michele Filippone
• Abstract summary: We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin-chain. Our results are based on Matrix Product Operator numerical simulations and agree with perturbative analytical calculations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 non-trivial universal behavior close to the XX limit. It is controlled by the scattering length $L^*\propto V^{-2}$, where $V$ is the strength of the integrability breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasi-ballistic" 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.

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