Effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators
Effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators
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DOI：
10.1103/physrevresearch.3.033145
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发表时间：
2021-03
影响因子：
4.2
通讯作者：
K. Chinni;P. Poggi;I. Deutsch
中科院分区：
文献类型：
--
作者：
K. Chinni;P. Poggi;I. Deutsch
我们研究了弱微扰引入的混沌如何影响模拟量子模拟输出的可靠性。作为一个玩具模型，我们考虑Lipkin-Meshkov-Glick（LMG）模型。受序参量在热力学极限下的半经典行为的启发，我们提出了一种测量基态量子相变和与猝灭动力学相关的动力学量子相变的方法。我们表明，存在一个小的时间依赖性扰动可以呈现系统的动力学混沌。然后，我们表明，这些量子相变的临界点的估计，从量子模拟其动力学，是强大的存在这种混沌扰动，而系统的其他方面，如平均磁化强度是脆弱的，因此不能可靠地从这个模拟器中提取。这可以根据依赖于相空间的全局结构的模拟量与依赖于局部轨迹的模拟量来理解。
We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick (LMG) model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization are fragile, and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs. those that depend on local trajectories.