2019年12月
Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
Communications in Mathematical Physics
- ,
- 巻
- 372
- 号
- 3
- 開始ページ
- 951
- 終了ページ
- 962
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
We prove that a quantum spin chain with half-odd-integral spin cannot have a<br />
unique ground state with a gap, provided that the interaction is short ranged,<br />
translation invariant, and possesses time-reversal symmetry or ${\mathbb Z}_2<br />
\times {\mathbb Z}_2$ symmetry (i.e., the symmetry with respect to the $\pi$<br />
rotations of spins about the three orthogonal axes). The proof is based on the<br />
deep analogy between the matrix product state formulation and the<br />
representation of the Cuntz algebra in the von Neumann algebra $\pi({\mathcal<br />
A}_{R})''$ constructed from the ground state restricted to the right<br />
half-infinite chain.
unique ground state with a gap, provided that the interaction is short ranged,<br />
translation invariant, and possesses time-reversal symmetry or ${\mathbb Z}_2<br />
\times {\mathbb Z}_2$ symmetry (i.e., the symmetry with respect to the $\pi$<br />
rotations of spins about the three orthogonal axes). The proof is based on the<br />
deep analogy between the matrix product state formulation and the<br />
representation of the Cuntz algebra in the von Neumann algebra $\pi({\mathcal<br />
A}_{R})''$ constructed from the ground state restricted to the right<br />
half-infinite chain.
- ID情報
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- arXiv ID : arXiv:1808.08740