Excitations of critical quantum spin chains from non-equilibrium classical dynamics

We study critical quantum spin chains with spin 1/2 that are dual to the non-equilibrium dynamics of a classical spin chain coupled to a bath. One example is the Kawasaki dynamics of an Ising chain. We give the exact groundstates, and single magnon excitations. Solutions for the two-magnon spectra are derived via the Bethe Ansatz. We discuss the corresponding dynamical critical exponents, which suggest that these chains host multiple dynamics at low energy. We also discuss a generalization to higher dimensions.