Ivy and hops are pretty different when it comes to removing them from an area once they are established. The ivy tends to fragment MUCH more than the hops do so your potential to end up with more 'scraps' is a lot greater. With hops, the rhizomes are confined to the top 5-6 inches of the soil so if you start digging about a foot out from the center of the crown and try to dig a trench all the way around the crown, what you will generally run into is a periodic rhizome growing outward from and away from the center of the crown (see attached photo). If you planted your original rhizomes horizontally this 'spread' may be a little worse than if they were planted vertically. Once you've located one, try to undermine it out to it's termination point (they MAY grow out a few feet per year depending on your soil) and make sure to remove it all the way back to the crown. Do this all the way around each crown for best results. What you'll end up with may be a few portions of rhizomes that you missed that will start sprouting within a few weeks. Keep a good eye out and locate and dig them up, and you should be able to remove the great majority by summer. Any that you may have missed should be easy to identify and dig up next spring. Keep in mind of those you missed, they are just like newly planted rhizomes that don't have well developed root systems so they aren't that hard to remove (compared to the crown they came from).
