论文标题
通过共享循环表示形式以不同的量子自旋链中的二聚化和néel秩序
Dimerization and Néel order in different quantum spin chains through a shared loop representation
论文作者
论文摘要
旋转的基础状态-s $ s $抗铁磁链$ h_ \ textrm {af} $具有基于投影$ \ sqrt q = 2s+1 = 2 \ cosh（λ）$的平面$ q $ -State Potts模型。多方面关系在这里用于直接将翻译对称性破坏的不同形式联系起来，这些破坏在这两种模型的基础状态：$ h_ \ textrm {af} $ dimerization in $ s> 1/2 $，néel订单的$ h_ \ h_ \ textrm {xxz} $ a $ s> 1/2 $，售价为$ h_ \ textrm {xxzxz} $ 0 $ 0 $ 0 $ 0 $ 0 $ 0 $ 0。提出的结果包括：i）对结果的上述量子自旋系统的翻译，该系统最近由Duminil-Copin-Li-Manolescu证明了一系列二维随机群集模型，以及II）以与最近的结构证明相似的方式证明了对称性破坏的方式，该结构证明了相似的结构性证明，这些结构证明了相似的频率不佳的相位，而不是相似的相位范围的不连续性。总的来说，$ q = 4 $和$ q> 4 $之间变化的量子表现是从无间隙基态向一对差距且广泛不同的基态的过渡。
The ground states of the spin-$ S $ antiferromagnetic chain $H_\textrm{AF}$ with a projection-based interaction and the spin-$ 1/2$ XXZ-chain $ H_\textrm{XXZ} $ at anisotropy parameter $Δ=\cosh(λ) $ share a common loop representation in terms of a two-dimensional functional integral which is similar to the classical planar $Q$-state Potts model at $ \sqrt Q= 2S+1 =2\cosh(λ)$. The multifaceted relation is used here to directly relate the distinct forms of translation symmetry breaking which are manifested in the ground states of these two models: dimerization for $H_\textrm{AF}$ at all $S> 1/2$, and Néel order for $ H_\textrm{XXZ} $ at $λ>0$. The results presented include: i) a translation to the above quantum spin systems of the results which were recently proven by Duminil-Copin-Li-Manolescu for a broad class of two-dimensional random-cluster models, and ii) a short proof of the symmetry breaking in a manner similar to the recent structural proof by Ray-Spinka of the discontinuity of the phase transition for $Q>4$. Altogether, the quantum manifestation of the change between $Q=4$ and $Q>4$ is a transition from a gapless ground state to a pair of gapped and extensively distinct ground states.
