First with a sharp spade plunge a line on the border to sever the
rhizomes.
Then sever the stuff on your side of the line into foot square pieces
and pull or pry out. Keep your side from showing any green and go down
the line with the spade once or twice a year. That will get most of it.
Keep the rest under control as seen.
If you can work with your neighbor it's easier than just being ****ed
off and going it alone.