Lieb-Schultz-Mattis theorem for 1d quantum magnets with magnetic space group symmetries

Chang-Tse Hsieh^1*, Yuan Yao², Linhao Li³, Masaki Oshikawa³

¹Department of Physics, National Taiwan University, Taipei, Taiwan
²Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama, Japan
³Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba, Japan

* Presenter:Chang-Tse Hsieh, email:cthsieh@phys.ntu.edu.tw

The conventional Lieb-Schultz-Mattis (LSM) theorem states that a 1d antiferromagnetic spin chain with lattice-translation and spin-rotation symmetries cannot have a unique gapped ground state if the spin per unit cell is half-integral. Here we discuss various versions of the 1d LSM theorem involving magnetic space group symmetries, which apply to systems with a broader class of spin interactions, such as Dzyaloshinskii-Moriya interactions and chiral three-spin interactions.

Keywords: Lieb-Schultz-Mattis theorem, spin chains, magnetic space group, Dzyaloshinskii-Moriya interaction