论文标题
$ \ mathbb {z} _3 \ times \ mathbb {z} _3 $对称性
One-dimensional model for deconfined criticality with $\mathbb{Z}_3 \times \mathbb{Z}_3$ symmetry
论文作者
论文摘要
我们最近继续努力发现一维模型中脱合量子临界的示例。在这项工作中，我们调查了$ \ mathbb {z} _3 $ ferromagnet与带价键固体（VBS）订单的阶段之间的过渡，该阶段在带有$ \ mathbb {z} _3 \ times \ times \ times \ times \ mathbb {z} _3 _3 _3 $ Global Symmetry的自旋链中。我们研究了两个sublattices站点上具有交替射影表示的模型，从而使哈密顿量与具有su（3） - invariant Singlets特征的VBS顺序的确切可解决的点连接。这样的模型不承认系统典型的系统实现临界点的典型的Lieb-Schultz-Mattis定理。但是，我们发现了从VBS阶段直接过渡到$ \ Mathbb {Z} _3 $ Ferromagnet的证据。有限输入缩放数据与二阶或弱的一阶过渡一致。我们在参数空间中发现了一个可集成的晶格模型，显然描述了相变，其长度很长，相关长度为190878晶格间距。基于该模型的确切结果，我们提出过渡是极弱的一阶，并且是通过步行重新归一化组流量描述的DQCP家族的一部分。
We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a $\mathbb{Z}_3$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with $\mathbb{Z}_3\times\mathbb{Z}_3$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a $\mathbb{Z}_3$ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order, and is part of a family of DQCP described by walking of renormalization group flows.
