Excitation-number conservation in XXZ spin chains
= Excitation-number conservation in XXZ spin chains
{c}
{title2=$[H,\sum_nZ_n]=0$}
For $H=\sum_{m<n}c_{mn}(X_mX_n+Y_mY_n)+\gamma_{mn}Z_mZ_n$, Pauli <commutators> give cancellation between the $XX$ and $YY$ terms in $[H,Z_m+Z_n]$, while each $ZZ$ term commutes individually. Hence total spin magnetization is conserved. Local $Z_k$ controls preserve the same law, so dynamics split into fixed-excitation sectors even when a particular sector is controllable.