We study a model of spins 1/2 on a square lattice, generalizing the quantum compass model via the addition of perturbing Heisenberg interactions between nearest neighbors, and investigate its phase diagram and magnetic excitations. This model has motivations both from the field of strongly correlated systems with orbital degeneracy and from that of solid-state based devices proposed for quantum computing. We find that the high degeneracy of ground states of the compass model is fragile and changes into twofold degenerate ground states for any finite amplitude of Heisenberg coupling. By computing the spin structure factors of finite clusters with Lanczos diagonalization, we evidence a rich variety of phases characterized by Z2 symmetry, that are either ferromagnetic, C-type antiferromagnetic, or of Neel type, and analyze the effects of quantum fluctuations on phase boundaries. In the ordered phases the anisotropy of compass interactions leads to a finite excitation gap to spin waves. We show that for small nanoscale clusters with large anisotropy gap the lowest excitations are column-flip excitations that emerge due to Heisenberg perturbations from the manifold of degenerate ground states of the compass model. We derive an effective one-dimensional XYZ model which faithfully reproduces the exact structure of these excited states and elucidates their microscopic origin. The low energy column-flip or compass-type excitations are robust against decoherence processes and are therefore well designed for storing information in quantum computing. We also point out that the dipolar interactions between nitrogen-vacancy centers forming a rectangular lattice in a diamond matrix may permit a solid-state realization of the anisotropic compass-Heisenberg model.
Frustration and Entanglement in Compass and Spin-Orbital Models
我们回顾了轨道超交换和自旋轨道纠缠的内在挫折的后果。虽然海森堡微扰相互作用消除了罗盘模型中的挫折，但最低的柱状激发在纳米罗盘团簇中是稳健的，并且可能用于量子计算。纠缠的自旋轨道状态在某些情况下确定基态，而在其他情况下涉及激发态并导致可测量的结果，如在$R$ VO $_3$钙钛矿中。强自旋轨道耦合的在位纠缠产生了蜂窝晶格上具有丰富磁相图的受抑Kitaev-Heisenberg模型。挫折是在这里反映在空穴传播的变化，从相干的反铁磁体通过隐藏的准粒子在曲折和条纹阶段完全不相干的Kitaev自旋液体。
Competing magnetic interactions in spin-1/2 square lattice: hidden order in Sr$_2$VO$_4$
随着温度的降低，Sr $_2$ VO $_4$经历了两个结构相变，四方晶系到正交晶系到四方晶系，没有长程磁序。最近的实验表明，只有在非常低的温度下，Sr $_{2}$ VO $_{4}$才可能进入一些未知的长程磁序相，但没有正交畸变。结合相对论性密度泛函理论和扩展的自旋1/2罗盘海森堡模型，我们发现了一个具有高度竞争交换作用的反铁磁单条纹基态，其中包含不可忽略的层间耦合，使系统处于XY和海森堡图之间的交叉点.最引人注目的是，我们发现了一个强大的两个网站的“自旋罗盘”交换各向异性，这是减轻由正交畸变引起的自旋条纹顺序。基于这些结果，我们讨论了隐藏的顺序相的起源和自旋液体在低温下的可能形成。
Thermodynamic theory of square skyrmion lattice in tetragonal frustrated antiferromagnets
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS)（复杂系统理论物理中心，基础科学研究院）；National Research University “Higher School of Economics”（国立高等经济大学）；The Faculty of Physics of St. Petersburg State University（圣彼得堡国立大学物理系）
