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

A critical quantum spin 1/2 chain dual to the non-equilibrium Kawasaki dynamics of an Ising chain coupled to a bath is presented. We give the exact groundstates, and single magnon excitations. Solutions for the two-magnon spectra are derived via a Bethe ansatz scheme. We discuss the corresponding two-magnon continuums and dynamical critical exponents, the latter of which suggest that these chains host multiple dynamics at low energy.