论文标题
带有磁场的调制$ xyz $链中的相图和拓扑顺序
Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
论文作者
论文摘要
研究了$ xyz $抗磁性自旋 - $ 1/2 $链条，在存在均匀和交错的轴向磁场的情况下交换和各向异性耦合。使用Hartee-fock近似产生的有效二次费米汉顿式二次效率哈密顿量进行了分析。结合精确的和平均场方法，确定并计算了模型的地面相图上的局部和字符串顺序参数。我们发现了一个具有振荡弦顺序的拓扑阶段，其周期为四个晶格间距，此前尚未报告该模型。给出了字符串顺序模式的详细分析。与Lieb-Schultz-Mattis Theorem及其扩展，磁化强度的高原以及一些其他保存数量相吻合，该模型的特殊$ xxz $限制带有额外的$ u（1）$对称性。我们已经证明，在涂抹高原的$ xyz $链中，强大的振荡弦顺序参数连续连接到其$ xxz $限制。同样，作为拓扑顺序的附加属性，在该阶段，即使在$ u（1）$对称性的线上，非平凡的绕组数和零能量的局部Majorana边缘状态也是强大的。
The $XYZ$ antiferromagnetic spin-$1/2$ chain with alternation of the exchange and anisotropy couplings in the presence of uniform and staggered axial magnetic fields is studied. The analysis is done using the effective quadratic fermionic Hamiltonian resulting from the Hartee-Fock approximation. Combining the exact and the mean-field methods, the local and string order parameters on the ground-state phase diagram of the model are identified and calculated. We found a topological phase with oscillating string order with a period of four lattice spacings, not reported before for this model. A detailed analysis of patterns of the string order is given. The special $XXZ$ limit of the model with additional $U(1)$ symmetry brings about, in agreement with the Lieb-Schultz-Mattis theorem and its extensions, plateaux of magnetization and some additional conserving quantities. We have shown that in the $XYZ$ chain, where the plateaux are smeared, the robust oscillating string order parameter is continuously connected to its $XXZ$ limit. Also, the non-trivial winding number and zero-energy localized Majorana edge states, as additional attributes of topological order, are robust in that phase, even off the line of $U(1)$ symmetry.
