We studied quantum phase transitions in the antiferromagnetic dimerized spin-1/2 XY chain andvtwo-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden symmetries within the Landau paradigm. After mapping of the spin Hamiltonians onto the tight-binding models with Dirac or Majorana fermions and, when necessary, the mean-field approximation, the analysis can be done analytically. By utilizing duality transformations the calculation of nonlocal string order parameters is mapped onto the local order problem in some dual representation and done without further approximations. Calculated phase diagrams, phase boundaries, order parameters and their symmetries for each of the phases provide a comprehensive quantitative Landau description of the quantum critical properties of the models considered. Complementarily, the phases with hidden orders can also be distinguished by the Pontryagin (winding) numbers which we have calculated as well. This unified framework can be straightforwardly applied for various spin chains and ladders, topological insulators and superconductors. Applications to other systems are under way.
N-leg integer-spin ladders and tubes in commensurate external fields -Nonlinear sigma model approach-
本文研究了具有反铁磁链内耦合的N臂整数自旋梯和管的低能性质。在奇腿管，自动对焦横档耦合造成挫折。为了系统地处理所有梯和管，我们应用基于非线性西格玛模型的Sénéchal方法[Phys. Rev. B 52，15319（1995）]。这种策略在弱链间（梯级）耦合机制中是有效的。我们发现所有的阻挫管都具有六重简并自旋1的磁振子带，作为最低激发态，而其他的阶梯和管具有标准的三重简并带。我们还考虑了四种塞曼项的影响：均匀的，交错只沿梯级，只沿链，或两个方向。上述无场情形的预测意味着，由于双简并最低磁振子在阻挫管中的凝聚，足够强的均匀场产生双组分Tomonaga-Luttinger液体（TLL）。相反，在所有其他系统中，场诱导标准的单分量TLL。这一点得到了基于金兹伯格-朗道理论的对称性和玻色子化论点的支持。玻色化还表明，当均匀场变大，次低磁振子带接触零能线时，双分量TLL消失，出现单分量TLL。在磁化过程中，这种转变可以被观察到为尖点奇异性。对具有交错Zeeman项的一维AF自旋系统的分析表明，双简并横磁振子和单纵磁振子的出现对于具有弱交错场的一维AF自旋系统是普遍的.
Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
