Dynamics of a quantum phase transition in the Aubry-André-Harper model with p -wave superconductivity
Dynamics of a quantum phase transition in the Aubry-André-Harper model with p -wave superconductivity
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DOI：
10.1103/physrevb.103.104202
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发表时间：
2020-12
影响因子：
3.7
通讯作者：
Xianqi Tong;Ye-Ming Meng;Xunda Jiang;Chaohong Lee;G. Neto;Gao Xianlong
中科院分区：
文献类型：
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作者：
Xianqi Tong;Ye-Ming Meng;Xunda Jiang;Chaohong Lee;G. Neto;Gao Xianlong
研究了一维Aubry-Andr‘e-Harper模型的非平衡动力学，通过改变势强和慢猝灭和突然猝灭来实现p波超导电性。首先，通过线性降低势强V，研究了从局域相到临界相的慢猝灭动力学。局域化长度是有限的，标度遵循Kibble-Zurek机制。结果表明，二阶相变线的临界指数相同，关联长度为1，动力学指数为1.373，与Aubry-Andr‘e模型不同。其次，我们还研究了三个不同阶段之间的猝灭动力学：局域阶段、临界阶段和扩展阶段。在<V=0</sup>和<V</sup>的极限下，我们通过Loschmidt回波解析地研究了猝灭动力学。结果表明，如果初态和失超后的哈密顿量处于不同的位相，Loschmidt回波将在一定的时间间隔内消失。此外，我们还发现，如果初值处于临界阶段，则猝灭的方向与前面提到的两个极限之一相同，并且会出现类似的行为。
We investigate the nonequilibrium dynamics of the one-dimension Aubry-Andr\'e-Harper model with $p$-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from the localized phase to the critical phase by linearly decreasing the potential strength $V$. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent $z\ensuremath{\nu}$, giving the correlation length $\ensuremath{\nu}=1$ and dynamical exponent $z=1.373\ifmmode\pm\else\textpm\fi{}0.023$, which are different from the Aubry-Andr\'e model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of $V=0$ and $V=\ensuremath{\infty}$, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of quenching is the same as one of the two limits mentioned before, and similar behaviors will occur.