Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
Abstract
We demonstrate the existence of a special chiral "phantom" mode with some analogy to a Goldstone mode in the anisotropic quantum X X Z Heisenberg spin chain. The phantom excitations contribute zero energy to the eigenstate, but a finite fixed quantum of momentum k_{0}. The mode exists not due to symmetry principles, but results from nontrivial scattering properties of magnons with momentum k_{0} given by the anisotropy via cosk_{0}=Δ . Different occupations of the phantom mode lead to energetical degeneracies between different magnetization sectors in the periodic case. This mode originates from special stringtype solutions of the Bethe ansatz equations with unbounded rapidities, the phantom Bethe roots (PBRs). We derive criteria under which the spectrum contains eigenstates with PBRs, both in open and periodically closed integrable systems, for spin1 /2 and higher spins, and discuss the respective chiral eigenstates. The simplest of such eigenstates, the spin helix state, which is a periodically modulated state of chiral nature, is built up from the phantom excitations exclusively. Implications of our results for experiments are discussed.
 Publication:

Physical Review B
 Pub Date:
 August 2021
 DOI:
 10.1103/PhysRevB.104.L081410
 arXiv:
 arXiv:2102.03295
 Bibcode:
 2021PhRvB.104h1410P
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 6 pages, 1 Figure, the version accepted by Letters to PRB