Phantom Bethe excitations and spin helices in integrable spin chains

We demonstrate the existence of a special chiral “phantom” mode with some analogy to a Goldstone mode in the anisotropic quantum XXZ Heisenberg spin chain. The phantom excitations contribute zero energy to the eigenstate, but a finite fixed quantum of momentum. The mode exists not due to symmetry principles, but results from nontrivial scattering properties of magnons with momentum k given by the anisotropy via cos (k) = Jz/Jx. The mode originates from special string-type solutions of the Bethe ansatz equations with unbounded rapidities, the phantom Bethe roots. All such Bethe states are chiral (the simplest representative being factorized state with helicoidal magnetization profile) and exist in both periodic and open XXZ spin chain under fine-tuning. I show how phantom Bethe states can be generated dissipatively, by setting a polarization gradient via coupling the ends of the open spin chain to suitable dissipative baths. Spin helix eigenstates were observed and used in recent cold atom experiments, and led to further surprising findings.