Puppy is right. I've read and studied a lot about breakups and infidelity. All walk away spouses fail to appreciate the depth of bond that years and years of marriage creates. If you really withold yourself, after a few months of no contact, or nearly no contact, a "vacuum" begins to grow in your spouse's mind. This is the place you used to occupy. It takes time for that vacuum to slowly expand, creating more and more pressure and anxiety. Things will remind them of you, and the vacuum gets stronger. If there was enough good between the two of you during your M, eventually that vacuum might become unbearable, and if you give them no other option, they'll beg to reconcile, just to alleviate that terrible anxiety. Doesn't mean reconciliation is guaranteed to succeed, but it does give you leverage to demand certain conditions. Once you let them back in, the anxiety is reduced, and then the real work begins.
Of course the rub is that you need to endure the vacuum feeling as well, and you need to be stronger than them!
