Time scaling of entanglement in integrable scale-invariant theories

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 in which the scale invariance is anisotropic between time and space, parametrized by z, most of the entanglement is carried by the slow modes. 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^{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 and find extremely good agreement. We show that due to the dominance of the slow modes in these non-relativistic theories, local quantum information is scrambled independent of z in a stronger way, compared to their relativistic counterparts.