论文标题
量子自旋链中的不对称价值 - 固定状态：奇数甚至旋转之间的差异
The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins
论文作者
论文摘要
Spin $ s $ s $ Quantum抗铁磁链的低能特性的定性差异与整数$ s $和Haldd-Odd-Integer $ S $ S $可以直观地理解为由Affleck，Kennedy，Lieb和Tasaki提出的价值债券图片。在这里，我们对具有奇数$ s $甚至$ s $的链之间的质差进行了类似直观的图解解释，这是对对称性保护拓扑（SPT）阶段的核心。 更确切地说，我们定义了一个国家的国家家庭，我们称之为不对称的价键固体（VBS）状态，该状态在Affleck-Kennedy-lieb-Tasaki（AKLT）状态（AKLT）状态与量子旋转链中的零态链中不断插入，该状态具有$ s = 1 $和2个状态。它始终具有指数衰减的截短相关函数，并且是短距哈密顿量的独特凹陷状态。我们还观察到，不对称的VBS状态具有$ \ mathbb {z} _2 \ times \ times \ mathbb {z} _2 $的$ \ mathbb {z} _2 $，而$ s = 2 $的中性反转对称性，但不适合$ s = 1 $。这与已知的事实是一致的：如果$ s = 2 $，则AKLT模型属于微不足道的SPT相位，如果$ s = 1 $，则属于非平凡的SPT相。尽管这种无序状态的插值家族已经知道，但我们的构造是统一的，是基于简单的物理图片。它还扩展到具有一般整数$ s $的旋转链，并为我们提供了对具有奇数甚至旋转模型之间的本质区别的直观解释。
The qualitative difference in low-energy properties of spin $S$ quantum antiferromagnetic chains with integer $S$ and half-odd-integer $S$ discovered by Haldane can be intuitively understood in terms of the valence-bond picture proposed by Affleck, Kennedy, Lieb, and Tasaki. Here we develop a similarly intuitive diagrammatic explanation of the qualitative difference between chains with odd $S$ and even $S$, which is at the heart of the theory of symmetry-protected topological (SPT) phases. More precisely, we define one-parameter families of states, which we call the asymmetric valence-bond solid (VBS) states, that continuously interpolate between the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and the trivial zero state in quantum spin chains with $S=1$ and 2. The asymmetric VBS state is obtained by systematically modifying the AKLT state. It always has exponentially decaying truncated correlation functions and is a unique gapped ground state of a short-ranged Hamiltonian. We also observe that the asymmetric VBS state possesses the time-reversal, the $\mathbb{Z}_2\times\mathbb{Z}_2$, and the bond-centered inversion symmetries for $S=2$, but not for $S=1$. This is consistent with the known fact that the AKLT model belongs to the trivial SPT phase if $S=2$ and to a nontrivial SPT phase if $S=1$. Although such interpolating families of disordered states were already known, our construction is unified and is based on a simple physical picture. It also extends to spin chains with general integer $S$ and provides us with an intuitive explanation of the essential difference between models with odd and even spins.
