Mutual information across the commensurate--incommensurate crossover and near the Kosterlitz--Thouless point of the spin-$\tfrac12$ $J_1$--$J_2$ Heisenberg chain

What quantum mutual information adds to conventional correlation functions is often unclear. We study the spin-1/2 $J_1$-$J_2$ Heisenberg chain, using DMRG on infinite chains and periodic rings and an SU(2) decomposition of the mutual information into correlation channels. For singlet ground states