Lieb Schultz Mattis Type Theorems for Quantum Spin Chains Without Continuous Symmetry
Lieb Schultz Mattis Type Theorems for Quantum Spin Chains Without Continuous Symmetry
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不连续对称的量子自旋链的 Lieb Schultz Mattis 型定理
DOI：
10.1007/s00220-019-03343-5
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发表时间：
2019
影响因子：
2.4
通讯作者：
Ogata Tasaki
中科院分区：
文献类型：
--
作者：
Moon Alvin;Ogata Yoshiko;Ogata Yoshiko;Ogata Tasaki
我们证明了具有半奇整数自旋的量子自旋链不可能有唯一的带隙基态，只要相互作用是短程的，平移不变的，并且具有时间反演对称性或对称性（即，关于自旋绕三个正交轴的旋转的对称性）。证明是基于矩阵乘积状态公式和从限制于右半无限链的基态构造的von Neumann代数中的Cuntz代数的表示之间的深刻类比。
We prove that a quantum spin chain with half-odd-integral spin cannot have a unique ground state with a gap, provided that the interaction is short ranged, translation invariant, and possesses time-reversal symmetry orsymmetry (i.e., the symmetry with respect to therotations of spins about the three orthogonal axes). The proof is based on the deep analogy between the matrix product state formulation and the representation of the Cuntz algebra in the von Neumann algebraconstructed from the ground state restricted to the right half-infinite chain.