Entanglement Entropy Bounds for Droplet States of the XXZ Model on the Strip

The scaling behavior of the entanglement entropy of droplet states in Heisenberg spin-1/2 XXZ model defined on a strip of width $M$ under the presence of a non-negative background magnetic field is investigated. Without any assumptions on $V$, a logarithmically corrected area law is shown. Assuming that the values of $V$ are i.i.d. random variables, an area law in expectation is obtained.