严格手征自旋液体与红宝石晶格上Gamma矩阵模型的平均场微扰
Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
摘要：
我们从理论上研究了红宝石晶格上Kitaev自旋模型的一个精确可解的Gamma矩阵推广，红宝石晶格是一个具有“扩展”顶点和链接的蜂窝晶格。我们发现这个模型显示了一个异常丰富的相图，其中包括：（i）无隙相稳定的自旋费米面，（ii）无隙相低能量狄拉克锥和二次带接触点，和（iii）有隙相有限陈数拥有值{ \pm }4，{ \pm }3，{ \pm }2和{ \pm }1。然后，该模型被推广到包括伊辛样的相互作用，打破了精确的可解性的模型在一个控制的方式。当这些条款是占主导地位的，它们导致一个平凡的伊辛有序相，这被证明是一个很大的耦合限制的精确可解的阶段。当这些相互作用是弱的限制，我们对待他们的平均场论，并提出由此产生的相图。我们讨论了不同阶段之间的过渡的性质。我们的结果突出了在密切相关的磁系统中可能的基态的丰富性。
英文摘要：
We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.
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