论文标题
二阶拓扑相变的紧急弹性的一般理论
General theory of emergent elasticity for second-order topological phase transitions
论文作者
论文摘要
Landau [1]对对称性破坏机制的提升是相变研究中的地标。 kosterlitz-无尽的相变[2-3]和分数量子霍尔效应[4]被认为是由另一种机制诱导的：拓扑变化。尽管拓扑秩序的理论迅速发展[5-7]，但看不见一个统一的理论框架，描述了这种新的相变范式及其与Landau范式的关系。在这里，我们基于变异原理建立了这样的框架，并表明任何二阶拓扑相变的临界条件是自由能拓扑受保护的二阶变化的正定性的丧失。对现场解决方案的拓扑保护的变化是针对其新兴位移进行的，该变化是通过为解决方案构造出现的弹性问题而引入的。相变的Landau范式研究全球性质变化引起的不稳定性，而拓扑相转换研究局部特性变化诱导的拓扑不稳定。该标准的总体有效性是通过分析两个真实空间中几种原型解（正弦模型的两键溶液的拓扑稳定性；手性磁铁中的孤立的天空敏化）和互相空间（单位链和diotomic链的声音光谱； diotomic链和diatotomic链的频谱；在kronig shoce ne kronig shorig shone kronig shone kronig-pean nyny kronig-pean nyny ny kronig pean nyny模型。每个磁场都是弹性的，具有空间调制的刚度，并且拓扑特性的变化在其软点处发生。我们预计我们的工作将成为对所有领域理论中拓扑相变的一般研究的起点。
The raise of the symmetry breaking mechanism by Landau[1] is a landmark in the studies of phase transitions. The Kosterlitz-Thouless phase transition[2-3] and the fractional quantum Hall effect[4], however, are believed to be induced by another mechanism: topology change. Despite rapid development of the theory of topological orders[5-7], a unified theoretical framework describing this new paradigm of phase transition and its relation to the Landau paradigm, is not seen. Here, we establish such a framework based on variational principle, and show that the critical condition for any second-order topological phase transitions is loss of positive-definiteness of a topologically protected second-order variation of the free energy. A topologically protected variation of a field solution is performed with respect to its emergent displacements, which is introduced by constructing an emergent elasticity problem for the solution. The Landau paradigm of phase transitions studies global property changes induced instability, while topological phase transitions study local property changes induced topological instability. The general effectiveness of this criterion is shown through analyzing the topological stability of several prototype solutions in both real space (two-kink solutions of the sine-Gordon model; an isolated skyrmion in chiral magnets) and reciprocal space (phonon spectrum of a monoatomic chain and a diatomic chain; band structure of a monoatomic chain within the Kronig-Penny model). Every field is emergent elastic with spatially modulated stiffness, and changes of topological property occur at its softened points. We anticipate our work to be a starting point for a general study of topological phase transitions in all field theories.
