Unifying topological phase transitions in non-interacting, interacting, and periodically driven systems
Unifying topological phase transitions in non-interacting, interacting, and periodically driven systems
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DOI：
10.1209/0295-5075/128/36001
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
P. Molignini;R. Chitra;Wei Chen;Wei Chen
中科院分区：
文献类型：
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作者：
P. Molignini;R. Chitra;Wei Chen;Wei Chen
拓扑相变发生在真实的材料以及量子工程系统中，所有这些在维度、对称性、相互作用和驱动方面都有很大差异，因此需要各种技术和概念来描述它们的拓扑性质。例如，拓扑可以从单粒子布洛赫波函数、绿色函数或多体波函数中获得。我们证明，尽管这种多样性，所有的拓扑相变显示一个普遍的功能：即，发散的曲率函数，组成的拓扑不变量在临界点。这个特性可以通过类似重整化群的方法来描述拓扑相变。这种方法扩展了朗道理论中的相关函数、临界指数、标度律和普适性类等概念，从而统一地描述了拓扑相变。
Topological phase transitions occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and driving, and hence require a variety of techniques and concepts to describe their topological properties. For instance, topology may be accessed from single-particle Bloch wave functions, Green's functions, or many-body wave functions. We demonstrate that despite this diversity, all topological phase transitions display a universal feature: namely, a divergence of the curvature function that composes the topological invariant at the critical point. This feature can be exploited via a renormalization-group–like methodology to describe topological phase transitions. This approach serves to extend notions of correlation function, critical exponents, scaling laws and universality classes used in Landau theory to characterize topological phase transitions in a unified manner.