Title says it all really.. Why is the XX spin chain a free fermion (non-interacting) model, and the XXZ chain not?
Is it right that ∑la†lal+1 isn't an interaction between fermions because it's creating a fermion on one site and destroying it on another? But why is ∑la†lala†l+1al+1 an interaction term?
Is something like
H1=−∑l(J+(−1)lK)(σxlσxl+1+σylσyl+1)
a free fermion model? If not, why not?
Edit I don't have enough reputation to set a bounty, but if anyone could answer this question, I'd be very grateful!
Edit 2 Anyone?
This post imported from StackExchange Physics at 2014-06-06 02:45 (UCT), posted by SE-user user6050