具有质量猝灭的自由费米子的电路复杂性
Circuit complexity for free Fermion with a mass quench
摘要：
利用Hackl $et\, al.$最近提出的计算自由费米子高斯态复杂性的方法，我们计算了狄拉克真空态的复杂性，以及具有质量猝灭的费米系统的激发态的复杂性.首先，我们回顾了Hackl的$et\, al.$给出的计数方法，并证明了该方法适用于所有的紧变换群$G$ .然后，我们利用这个结果来研究这些状态的复杂性的时间演化。我们表明，对于旋转不变的参考态，总的复杂性的到来的真空状态将饱和的瞬时真空状态的值在后期的时间，与一个典型的时间尺度，以达到最终的稳定状态。此外，我们还发现在突然猝灭下的复杂性增长与质量差成正比，这与具有激波的AdS-Vaidya黑洞中的全息图复杂性增长率具有相似的行为，即使对偶边界CFT是强耦合的.最后，我们得到了激发态和非转动参考态的一些性质。
英文摘要：
By using a recent approach proposed by Hackl $et\, al.$ to evaluate the complexity of the free fermionic Gaussian state, we compute the complexity of the Dirac vacuum state as well as the excited state of the Fermi system with a mass quench. First of all, we review the counting method given by Hackl $et\, al.$, and demonstrate that the result can be adapted to all of the compact transformation group $G$. Then, we utilize this result to study the time evolution of the complexity of these states. We show that, for the rotational invariant reference state, the total complexity of the incoming vacuum state will saturate the value of the instantaneous vacuum state at the late time, with a typical timescale to achieve the final stable state. Moreover, we find that the complexity growth under the sudden quench is directly proportional to the mass difference, which shares similar behaviors with the holograph complexity growth rate in an AdS-Vaidya black hole with a shock wave, even though the dual boundary CFT is strongly coupled. Finally, we obtain some features of the excited state and the non-rotational reference state.
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