# 1 D lattice

 P: 2 I have a question if you have an Hamiltonian given by $H = \sum_{i,i+1} \sigma_i \cdot \sigma_{i+1}$ where i can even or odd bonds so in a 1D lattice so if you have 4 sites(1 2 3 4 1) then (12) and (34) are even bonds and (23) and (41) are odd bonds. and I was checking if $[H_{x even(12)} , H_{x even(34)}]$ will they commute also do even and odd bonds commute i.e. $[H_{x even} , H_{x odd}]$