曲率函数重正化、拓扑相变和多临界性
Curvature function renormalisation, topological phase transitions and multicriticality
摘要：
最近提出的拓扑相变的曲率重整化群方案定义了一个通用的“曲率函数”作为理论参数的函数，并表明拓扑相变是由该函数在某些参数值处的发散发出信号的，称为临界点，与通常的相变类似。一个重整化群过程也被引入作为一种方式，从临界点流向一个固定点，在适当定义的关联函数趋于零和拓扑量子数表征相位是很容易计算的。在本文中，使用两个独立的模型-在AIII对称类的模型和BDI对称类的模型-在一维作为例子，我们表明，有情况下，不动点曲线和临界点曲线出现相交，原来是多临界点，并专注于理解其含义。
英文摘要：
A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic `curvature function' as a function of the parameters of the theory and shows that topological phase transitions are signalled by the divergence of this function at certain parameters values, called critical points, in analogy with usual phase transitions. A renormalization group procedure was also introduced as a way of flowing away from the critical point towards a fixed point, where an appropriately defined correlation function goes to zero and topological quantum numbers characterising the phase are easy to compute. In this paper, using two independent models - a model in the AIII symmetry class and a model in the BDI symmetry class - in one dimension as examples, we show that there are cases where the fixed point curve and the critical point curve appear to intersect, which turn out to be multi-critical points, and focus on understanding its implications.
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