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arXiv · 2106.14700

On the Time Scaling of Entanglement in Integrable Scale-Invariant Theories

M. Reza Mohammadi Mozaffar·Ali Mollabashi
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Abstract

In two dimensional isotropic scale invariant theories, the time scaling of the entanglement entropy of a segment is fixed via the conformal symmetry. We consider scale invariance in a more general sense and show that in integrable theories that the scale invariance is anisotropic between time and space, parametrized by $z$, most of the entanglement is carried by the slow modes for $z>1$. At early times entanglement grows linearly due to the contribution of the fast modes, before smoothly entering a slow mode regime where it grows forever with $t^{\frac{1}{1-z}}$. The slow mode regime admits a logarithmic enhancement in bosonic theories. We check our analytical results against numerical simulations in corresponding fermionic and bosonic lattice models finding extremely good agreement. We show that in these non-relativistic theories that the slow modes are dominant, local quantum information is universally scrambled in a stronger way compared to their relativistic counterparts.

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M. Reza Mohammadi Mozaffar, Ali Mollabashi. 2021-06-28. On the Time Scaling of Entanglement in Integrable Scale-Invariant Theories. https://arxiv.org/abs/2106.14700

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