I bring mine inside & leave in the pot & just let them die off over the winter.
They will come back next spring. But mine did not bloom, just green leaves.
Other people dig them up, clean off the tubers, let them dry & store for the winter.

I apologize, I called them tubers, instead of rhizomes.

Most of mine winter over in the ground here, but they are easy to carry over in pots. I just wait for the first frost to knock back the tops, cut them back to an inch or so of stem, and put the pots in a place where they'll be cool, but won't freeze solid (an unheated garage or basement works well.) Definitely no fertilizer until spring, and very little water - they should be almost dry. I water them maybe once a month during the winter. They could be kept in growth in a heated greenhouse, but in a home there would not be enough light for healthy growth, let alone bloom. Best to give them a rest for the winter and repot or top dress the plants in spring.

Plants that don't bloom the next year aren't getting enough sun, water, or food (they love compost) during the growing season. Rhizomes can get really crowded in pots and exhaust their food supplies rapidly, so I'd divide and replant them at least every other year.

I drag my pots into the basement, and basically ignore them. Around March (?), I'll see new sprouts shooting through the dried up soil. Amazing plants! I might start giving some occasional water at that point, but not too much. When it's time to plant out, I definitely divide the biggest clumps, or they will explode the pots.