フルヤ　シュンスケ   FURUYA Shunsuke   古谷　峻介    所属   埼玉医科大学  医学部 教養教育    職種   専任講師
論文種別	学術雑誌(原著)
言語種別	英語
査読の有無	査読あり
表題	Translation constraints on quantum phases with twisted boundary conditions
掲載誌名	正式名：PHYSICAL REVIEW B ISSNコード：2469-9950/2469-9969
出版社	AMER PHYSICAL SOC
巻・号・頁	100(17)
著者・共著者	Shunsuke C. Furuya,Yusuke Horinouchi
発行年月	2019/11
概要	Bulk properties of quantum phases should be independent of a specific choice of boundary conditions as long as the boundary respects the symmetries. Based on this physically reasonable requirement, we discuss the Lieb-Schultz-Mattis-type ingappability in two-dimensional quantum magnets under a boundary condition that makes evident a quantum anomaly underlying the lattice system. In particular, we direct our attention to those on the checkerboard lattice, which are closely related to frustrated quantum magnets on the square lattice and on the Shastry-Sutherland lattice. Our discussion is focused on the adiabatic U(1) flux insertion through a closed path in a boundary condition twisted by a spatial rotation and a reflection. Two-dimensional systems in this boundary condition are effectively put on a nonorientable space, namely the Klein bottle. We show that the translation symmetry on the Klein-bottle space excludes the possibility of the unique and gapped ground state. Taking advantage of the flux insertion argument, we also discuss the ground-state degeneracy on magnetization plateaus of the Heisenberg antiferromagnet on the checkerboard lattice.
DOI	10.1103/PhysRevB.100.174435