引力奇点
非平衡态热力学
物理
对数
拓扑(电路)
绕组编号
相变
相(物质)
光谱(功能分析)
动力系统理论
统计物理学
数学
量子力学
组合数学
数学分析
作者
Szabolcs Vajna,Balázs Dóra
出处
期刊:Physical Review B
[American Physical Society]
日期:2015-04-17
卷期号:91 (15)
被引量:180
标识
DOI:10.1103/physrevb.91.155127
摘要
We study the nonequilibrium time evolution of a variety of one-dimensional (1D) and two-dimensional (2D) systems (including SSH model, Kitaev-chain, Haldane model, $p+ip$ superconductor, etc.) following a sudden quench. We prove analytically that topology-changing quenches are always followed by nonanalytical temporal behavior of return rates (logarithm of the Loschmidt echo), referred to as dynamical phase transitions (DPTs) in the literature. Similarly to edge states in topological insulators, DPTs can be classified as being topologically protected or not. In 1D systems the number of topologically protected nonequilibrium time scales are determined by the difference between the initial and final winding numbers, while in 2D systems no such relation exists for the Chern numbers. The singularities of dynamical free energy in the 2D case are qualitatively different from those of the 1D case; the cusps appear only in the first time derivative.
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