Title: Entanglement scaling and spatial correlations of the transverse field Ising model with perturbations,
Abstract: We study numerically the entanglement entropy and spatial correlations of the
one dimensional transverse field Ising model with three different
perturbations. First, we focus on the out of equilibrium, steady state with an
energy current passing through the system. By employing a variety of
matrix-product state based methods, we confirm the phase diagram and compute
the entanglement entropy. Second, we consider a small perturbation that takes
the system away from integrability and calculate the correlations, the central
charge and the entanglement entropy. Third, we consider periodically weakened
bonds, exploring the phase diagram and entanglement properties first in the
situation when the weak and strong bonds alternate (period two-bonds) and then
the general situation of a period of n bonds. In the latter case we find a
critical weak bond that scales with the transverse field as $J'_c/J$ =
$(h/J)^n$, where $J$ is the strength of the strong bond, $J'$ of the weak bond
and $h$ the transverse field. We explicitly show that the energy current is not
a conserved quantity in this case.